On the numerical range behavior under the generalized Aluthge transform

David E.V. Rose; Ilya M. Spitkovsky

doi:10.1080/03081080701264671

On the numerical range behavior under the generalized Aluthge transform

David E.V. Rose, Ilya M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A = UR be the (right) polar decomposition of an nn matrix A. The generalized Aluthge transform is then given by [image omitted]. We investigate the behavior of the numerical range W((A)), and in particular its boundary, as a function of . We obtain complete results in the 22 case, when W((A)) can be described explicitly, and then discuss which of the established properties persist in the general setting.

Original language	English (US)
Pages (from-to)	163-177
Number of pages	15
Journal	Linear and Multilinear Algebra
Volume	56
Issue number	1-2
DOIs	https://doi.org/10.1080/03081080701264671
State	Published - Jan 2008

Keywords

Aluthge transform
Numerical range

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081080701264671

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title = "On the numerical range behavior under the generalized Aluthge transform",

abstract = "Let A = UR be the (right) polar decomposition of an nn matrix A. The generalized Aluthge transform is then given by [image omitted]. We investigate the behavior of the numerical range W((A)), and in particular its boundary, as a function of . We obtain complete results in the 22 case, when W((A)) can be described explicitly, and then discuss which of the established properties persist in the general setting.",

keywords = "Aluthge transform, Numerical range",

author = "Rose, {David E.V.} and Spitkovsky, {Ilya M.}",

note = "Funding Information: The work on this article was started in the summer of 2005 during the REU program at the College of William and Mary and was then supported by NSF Grant DMS-0353510. During its completion both authors were supported in part by NSF Grant DMS-0456625. The results were presented at the 8th Workshop on Numerical Ranges and Numerical Radii, Universit{\"a}t Bremen, Germany, July 15–17, 2006.",

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AU - Spitkovsky, Ilya M.

N1 - Funding Information: The work on this article was started in the summer of 2005 during the REU program at the College of William and Mary and was then supported by NSF Grant DMS-0353510. During its completion both authors were supported in part by NSF Grant DMS-0456625. The results were presented at the 8th Workshop on Numerical Ranges and Numerical Radii, Universität Bremen, Germany, July 15–17, 2006.

PY - 2008/1

Y1 - 2008/1

N2 - Let A = UR be the (right) polar decomposition of an nn matrix A. The generalized Aluthge transform is then given by [image omitted]. We investigate the behavior of the numerical range W((A)), and in particular its boundary, as a function of . We obtain complete results in the 22 case, when W((A)) can be described explicitly, and then discuss which of the established properties persist in the general setting.

AB - Let A = UR be the (right) polar decomposition of an nn matrix A. The generalized Aluthge transform is then given by [image omitted]. We investigate the behavior of the numerical range W((A)), and in particular its boundary, as a function of . We obtain complete results in the 22 case, when W((A)) can be described explicitly, and then discuss which of the established properties persist in the general setting.

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On the numerical range behavior under the generalized Aluthge transform

Abstract

Keywords

ASJC Scopus subject areas

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