Syndetic Sensitivity and Mean Sensitivity for Linear Operators

We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Quanquan Yao [verfasserIn] Peiyong Zhu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	syndetically sensitive cofinitely sensitive mean sensitive

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 11(2023), 13, p 2796
Übergeordnetes Werk:	volume:11 ; year:2023 ; number:13, p 2796

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math11132796

Katalog-ID:	DOAJ093997833

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520			\|a We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations.
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Indexfelder

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callnumber-subject-code	QA
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allfields	10.3390/math11132796 doi (DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4 DE-627 ger DE-627 rakwb eng QA1-939 Quanquan Yao verfasserin aut Syndetic Sensitivity and Mean Sensitivity for Linear Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations. syndetically sensitive cofinitely sensitive mean sensitive Mathematics Peiyong Zhu verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 13, p 2796 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:13, p 2796 https://doi.org/10.3390/math11132796 kostenfrei https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 kostenfrei https://www.mdpi.com/2227-7390/11/13/2796 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 13, p 2796
spelling	10.3390/math11132796 doi (DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4 DE-627 ger DE-627 rakwb eng QA1-939 Quanquan Yao verfasserin aut Syndetic Sensitivity and Mean Sensitivity for Linear Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations. syndetically sensitive cofinitely sensitive mean sensitive Mathematics Peiyong Zhu verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 13, p 2796 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:13, p 2796 https://doi.org/10.3390/math11132796 kostenfrei https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 kostenfrei https://www.mdpi.com/2227-7390/11/13/2796 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 13, p 2796
allfields_unstemmed	10.3390/math11132796 doi (DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4 DE-627 ger DE-627 rakwb eng QA1-939 Quanquan Yao verfasserin aut Syndetic Sensitivity and Mean Sensitivity for Linear Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations. syndetically sensitive cofinitely sensitive mean sensitive Mathematics Peiyong Zhu verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 13, p 2796 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:13, p 2796 https://doi.org/10.3390/math11132796 kostenfrei https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 kostenfrei https://www.mdpi.com/2227-7390/11/13/2796 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 13, p 2796
allfieldsGer	10.3390/math11132796 doi (DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4 DE-627 ger DE-627 rakwb eng QA1-939 Quanquan Yao verfasserin aut Syndetic Sensitivity and Mean Sensitivity for Linear Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations. syndetically sensitive cofinitely sensitive mean sensitive Mathematics Peiyong Zhu verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 13, p 2796 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:13, p 2796 https://doi.org/10.3390/math11132796 kostenfrei https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 kostenfrei https://www.mdpi.com/2227-7390/11/13/2796 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 13, p 2796
allfieldsSound	10.3390/math11132796 doi (DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4 DE-627 ger DE-627 rakwb eng QA1-939 Quanquan Yao verfasserin aut Syndetic Sensitivity and Mean Sensitivity for Linear Operators 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations. syndetically sensitive cofinitely sensitive mean sensitive Mathematics Peiyong Zhu verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 13, p 2796 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:13, p 2796 https://doi.org/10.3390/math11132796 kostenfrei https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 kostenfrei https://www.mdpi.com/2227-7390/11/13/2796 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 13, p 2796
language	English
source	In Mathematics 11(2023), 13, p 2796 volume:11 year:2023 number:13, p 2796
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title	Syndetic Sensitivity and Mean Sensitivity for Linear Operators
ctrlnum	(DE-627)DOAJ093997833 (DE-599)DOAJ8219cb2c24ef4543953c631009d980c4
title_full	Syndetic Sensitivity and Mean Sensitivity for Linear Operators
author_sort	Quanquan Yao
journal	Mathematics
journalStr	Mathematics
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lang_code	eng
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publishDateSort	2023
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author_browse	Quanquan Yao Peiyong Zhu
container_volume	11
class	QA1-939
format_se	Elektronische Aufsätze
author-letter	Quanquan Yao
doi_str_mv	10.3390/math11132796
author2-role	verfasserin
title_sort	syndetic sensitivity and mean sensitivity for linear operators
callnumber	QA1-939
title_auth	Syndetic Sensitivity and Mean Sensitivity for Linear Operators
abstract	We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations.
abstractGer	We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations.
abstract_unstemmed	We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< such that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<×</mo<<mi<Y</mi<<mo<,</mo<<mi<T</mi<<mo<×</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is cofinitely sensitive but <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<X</mi<<mo<,</mo<<mi<T</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< are not syndetically sensitive. For the mean sensitivity aspect, we show that if <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Y</mi<<mo<,</mo<<mi<S</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< is sensitive and not mean sensitive, where <i<Y</i< is a complex Banach space, the spectrum of <i<T</i< meets the unit circle. We also obtain some results regarding mean sensitive perturbations.
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title_short	Syndetic Sensitivity and Mean Sensitivity for Linear Operators
url	https://doi.org/10.3390/math11132796 https://doaj.org/article/8219cb2c24ef4543953c631009d980c4 https://www.mdpi.com/2227-7390/11/13/2796 https://doaj.org/toc/2227-7390
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up_date	2024-07-03T20:38:55.579Z
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