Complex Symmetric Toeplitz Operators
Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bu, Qinggang [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Integral equations and operator theory - Springer International Publishing, 1978, 93(2021), 2 vom: 12. März |
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| Übergeordnetes Werk: |
volume:93 ; year:2021 ; number:2 ; day:12 ; month:03 |
| Links: |
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| DOI / URN: |
10.1007/s00020-021-02629-5 |
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OLC2124322532 |
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| 520 | |a Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. | ||
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10.1007/s00020-021-02629-5 doi (DE-627)OLC2124322532 (DE-He213)s00020-021-02629-5-p DE-627 ger DE-627 rakwb eng 510 004 VZ 17,1 ssgn Bu, Qinggang verfasserin aut Complex Symmetric Toeplitz Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. Toeplitz operators Hardy space Complex symmetric operators Chen, Yong (orcid)0000-0002-7970-8778 aut Zhu, Sen aut Enthalten in Integral equations and operator theory Springer International Publishing, 1978 93(2021), 2 vom: 12. März (DE-627)129859184 (DE-600)282475-9 (DE-576)015166651 0378-620X nnns volume:93 year:2021 number:2 day:12 month:03 https://doi.org/10.1007/s00020-021-02629-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 AR 93 2021 2 12 03 |
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10.1007/s00020-021-02629-5 doi (DE-627)OLC2124322532 (DE-He213)s00020-021-02629-5-p DE-627 ger DE-627 rakwb eng 510 004 VZ 17,1 ssgn Bu, Qinggang verfasserin aut Complex Symmetric Toeplitz Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. Toeplitz operators Hardy space Complex symmetric operators Chen, Yong (orcid)0000-0002-7970-8778 aut Zhu, Sen aut Enthalten in Integral equations and operator theory Springer International Publishing, 1978 93(2021), 2 vom: 12. März (DE-627)129859184 (DE-600)282475-9 (DE-576)015166651 0378-620X nnns volume:93 year:2021 number:2 day:12 month:03 https://doi.org/10.1007/s00020-021-02629-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 AR 93 2021 2 12 03 |
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10.1007/s00020-021-02629-5 doi (DE-627)OLC2124322532 (DE-He213)s00020-021-02629-5-p DE-627 ger DE-627 rakwb eng 510 004 VZ 17,1 ssgn Bu, Qinggang verfasserin aut Complex Symmetric Toeplitz Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. Toeplitz operators Hardy space Complex symmetric operators Chen, Yong (orcid)0000-0002-7970-8778 aut Zhu, Sen aut Enthalten in Integral equations and operator theory Springer International Publishing, 1978 93(2021), 2 vom: 12. März (DE-627)129859184 (DE-600)282475-9 (DE-576)015166651 0378-620X nnns volume:93 year:2021 number:2 day:12 month:03 https://doi.org/10.1007/s00020-021-02629-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 AR 93 2021 2 12 03 |
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10.1007/s00020-021-02629-5 doi (DE-627)OLC2124322532 (DE-He213)s00020-021-02629-5-p DE-627 ger DE-627 rakwb eng 510 004 VZ 17,1 ssgn Bu, Qinggang verfasserin aut Complex Symmetric Toeplitz Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. Toeplitz operators Hardy space Complex symmetric operators Chen, Yong (orcid)0000-0002-7970-8778 aut Zhu, Sen aut Enthalten in Integral equations and operator theory Springer International Publishing, 1978 93(2021), 2 vom: 12. März (DE-627)129859184 (DE-600)282475-9 (DE-576)015166651 0378-620X nnns volume:93 year:2021 number:2 day:12 month:03 https://doi.org/10.1007/s00020-021-02629-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 AR 93 2021 2 12 03 |
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Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 |
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Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 |
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Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”. © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2124322532</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505094524.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00020-021-02629-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2124322532</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00020-021-02629-5-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bu, Qinggang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complex Symmetric Toeplitz Operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper aims to study when a Toeplitz operator $$T_\varphi $$ on the Hardy space $$H^2$$ of the unit disk is complex symmetric, that is, $$T_\varphi $$ admits a symmetric matrix representation relative to some orthonormal basis of $$H^2$$. For certain trigonometric symbols $$\varphi $$, we give necessary and sufficient conditions for $$T_\varphi $$ to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Toeplitz operators</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hardy space</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex symmetric operators</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chen, Yong</subfield><subfield code="0">(orcid)0000-0002-7970-8778</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhu, Sen</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Integral equations and operator theory</subfield><subfield code="d">Springer International Publishing, 1978</subfield><subfield code="g">93(2021), 2 vom: 12. März</subfield><subfield code="w">(DE-627)129859184</subfield><subfield code="w">(DE-600)282475-9</subfield><subfield code="w">(DE-576)015166651</subfield><subfield code="x">0378-620X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:93</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:2</subfield><subfield code="g">day:12</subfield><subfield code="g">month:03</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00020-021-02629-5</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2030</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">93</subfield><subfield code="j">2021</subfield><subfield code="e">2</subfield><subfield code="b">12</subfield><subfield code="c">03</subfield></datafield></record></collection>
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