Operators with real parts at least

For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a...
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Gespeichert in:

Autor*in:	Gau, Hwa-Long [verfasserIn] Wu, Pei Yuan

Format:	Artikel
Sprache:	Englisch

Erschienen:	2017

Rechteinformationen:	Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016

Schlagwörter:	47A20 47A12 numerical range 15A60 matrix Eigenvalues

Übergeordnetes Werk:	Enthalten in: Linear and multilinear algebra - Reading : Taylor & Francis, 1973, 65(2017), 10, Seite 1988-12
Übergeordnetes Werk:	volume:65 ; year:2017 ; number:10 ; pages:1988-12

Links:	Volltext Link aufrufen Link aufrufen

DOI / URN:	10.1080/03081087.2016.1267106

Katalog-ID:	OLC1997370190

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allfields	10.1080/03081087.2016.1267106 doi PQ20171228 (DE-627)OLC1997370190 (DE-599)GBVOLC1997370190 (PRQ)c1833-c5c3e6a6c91db871f0d2428c712f6385861c903eb893644e7ec5ece4d374f1a10 (KEY)0064897320170000065001001988operatorswithrealpartsatleast DE-627 ger DE-627 rakwb eng 510 DE-600 31.25 bkl Gau, Hwa-Long verfasserin aut Operators with real parts at least 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C. Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016 47A20 47A12 numerical range 15A60 matrix Eigenvalues Wu, Pei Yuan oth Enthalten in Linear and multilinear algebra Reading : Taylor & Francis, 1973 65(2017), 10, Seite 1988-12 (DE-627)129400602 (DE-600)186457-9 (DE-576)014783029 0308-1087 nnns volume:65 year:2017 number:10 pages:1988-12 http://dx.doi.org/10.1080/03081087.2016.1267106 Volltext http://www.tandfonline.com/doi/abs/10.1080/03081087.2016.1267106 https://search.proquest.com/docview/1954946185 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT 31.25 AVZ AR 65 2017 10 1988-12
spelling	10.1080/03081087.2016.1267106 doi PQ20171228 (DE-627)OLC1997370190 (DE-599)GBVOLC1997370190 (PRQ)c1833-c5c3e6a6c91db871f0d2428c712f6385861c903eb893644e7ec5ece4d374f1a10 (KEY)0064897320170000065001001988operatorswithrealpartsatleast DE-627 ger DE-627 rakwb eng 510 DE-600 31.25 bkl Gau, Hwa-Long verfasserin aut Operators with real parts at least 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C. Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016 47A20 47A12 numerical range 15A60 matrix Eigenvalues Wu, Pei Yuan oth Enthalten in Linear and multilinear algebra Reading : Taylor & Francis, 1973 65(2017), 10, Seite 1988-12 (DE-627)129400602 (DE-600)186457-9 (DE-576)014783029 0308-1087 nnns volume:65 year:2017 number:10 pages:1988-12 http://dx.doi.org/10.1080/03081087.2016.1267106 Volltext http://www.tandfonline.com/doi/abs/10.1080/03081087.2016.1267106 https://search.proquest.com/docview/1954946185 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT 31.25 AVZ AR 65 2017 10 1988-12
allfields_unstemmed	10.1080/03081087.2016.1267106 doi PQ20171228 (DE-627)OLC1997370190 (DE-599)GBVOLC1997370190 (PRQ)c1833-c5c3e6a6c91db871f0d2428c712f6385861c903eb893644e7ec5ece4d374f1a10 (KEY)0064897320170000065001001988operatorswithrealpartsatleast DE-627 ger DE-627 rakwb eng 510 DE-600 31.25 bkl Gau, Hwa-Long verfasserin aut Operators with real parts at least 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C. Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016 47A20 47A12 numerical range 15A60 matrix Eigenvalues Wu, Pei Yuan oth Enthalten in Linear and multilinear algebra Reading : Taylor & Francis, 1973 65(2017), 10, Seite 1988-12 (DE-627)129400602 (DE-600)186457-9 (DE-576)014783029 0308-1087 nnns volume:65 year:2017 number:10 pages:1988-12 http://dx.doi.org/10.1080/03081087.2016.1267106 Volltext http://www.tandfonline.com/doi/abs/10.1080/03081087.2016.1267106 https://search.proquest.com/docview/1954946185 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT 31.25 AVZ AR 65 2017 10 1988-12
allfieldsGer	10.1080/03081087.2016.1267106 doi PQ20171228 (DE-627)OLC1997370190 (DE-599)GBVOLC1997370190 (PRQ)c1833-c5c3e6a6c91db871f0d2428c712f6385861c903eb893644e7ec5ece4d374f1a10 (KEY)0064897320170000065001001988operatorswithrealpartsatleast DE-627 ger DE-627 rakwb eng 510 DE-600 31.25 bkl Gau, Hwa-Long verfasserin aut Operators with real parts at least 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C. Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016 47A20 47A12 numerical range 15A60 matrix Eigenvalues Wu, Pei Yuan oth Enthalten in Linear and multilinear algebra Reading : Taylor & Francis, 1973 65(2017), 10, Seite 1988-12 (DE-627)129400602 (DE-600)186457-9 (DE-576)014783029 0308-1087 nnns volume:65 year:2017 number:10 pages:1988-12 http://dx.doi.org/10.1080/03081087.2016.1267106 Volltext http://www.tandfonline.com/doi/abs/10.1080/03081087.2016.1267106 https://search.proquest.com/docview/1954946185 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT 31.25 AVZ AR 65 2017 10 1988-12
allfieldsSound	10.1080/03081087.2016.1267106 doi PQ20171228 (DE-627)OLC1997370190 (DE-599)GBVOLC1997370190 (PRQ)c1833-c5c3e6a6c91db871f0d2428c712f6385861c903eb893644e7ec5ece4d374f1a10 (KEY)0064897320170000065001001988operatorswithrealpartsatleast DE-627 ger DE-627 rakwb eng 510 DE-600 31.25 bkl Gau, Hwa-Long verfasserin aut Operators with real parts at least 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C. Nutzungsrecht: © 2016 Informa UK Limited, trading as Taylor & Francis Group 2016 47A20 47A12 numerical range 15A60 matrix Eigenvalues Wu, Pei Yuan oth Enthalten in Linear and multilinear algebra Reading : Taylor & Francis, 1973 65(2017), 10, Seite 1988-12 (DE-627)129400602 (DE-600)186457-9 (DE-576)014783029 0308-1087 nnns volume:65 year:2017 number:10 pages:1988-12 http://dx.doi.org/10.1080/03081087.2016.1267106 Volltext http://www.tandfonline.com/doi/abs/10.1080/03081087.2016.1267106 https://search.proquest.com/docview/1954946185 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT 31.25 AVZ AR 65 2017 10 1988-12
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abstract	For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C.
abstractGer	For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C.
abstract_unstemmed	For an -matrix ( ) A (a contraction with eigenvalues in the open unit disc and ), we consider the numerical range properties of . It is shown that W(B), the numerical range of B, is contained in the half-plane , its boundary contains exactly one line segment L, which lies on , and, for any in , is a subspace of dimension one with the property that are linearly independent for any nonzero vector x in M. Using such properties, we prove that any n-by-n matrix C with can be extended, under unitary similarity, to a direct sum of a diagonal matrix D with diagonals on the line and copies of B of the above type, and, moreover, if has a common point with , then C has B as a direct summand. This generalizes previous results of the authors for a nilpotent C.
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doi_str	10.1080/03081087.2016.1267106
up_date	2024-07-04T02:45:35.165Z
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