ON THE STAMPFLI POINT OF SOME OPERATORS AND MATRICES

Thanin Quartz; Ilya M. Spitkovsky

doi:10.7153/oam-2021-15-80

ON THE STAMPFLI POINT OF SOME OPERATORS AND MATRICES

Thanin Quartz, Ilya M. Spitkovsky

Mathematics

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

Abstract

The center of mass of an operator A (denoted St(A), and called in this paper as the Stampfli point of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique λ ∈ C delivering the minimum value of ‖A − λI‖. We derive some results concerning the location of St(A) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal A its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St(A)=0 and Roberts orthogonality of A to the identity operator are established.

Original language	English (US)
Article number	15-80
Pages (from-to)	1267-1287
Number of pages	21
Journal	Operators and Matrices
Volume	15
Issue number	4
DOIs	https://doi.org/10.7153/oam-2021-15-80
State	Published - Dec 2021

Keywords

Almost normal operators
Maximal numerical range
Roberts orthogonality
Stampfli point (center of mass) of operators

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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Cite this

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abstract = "The center of mass of an operator A (denoted St(A), and called in this paper as the Stampfli point of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique λ ∈ C delivering the minimum value of ‖A − λI‖. We derive some results concerning the location of St(A) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal A its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St(A)=0 and Roberts orthogonality of A to the identity operator are established.",

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N2 - The center of mass of an operator A (denoted St(A), and called in this paper as the Stampfli point of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique λ ∈ C delivering the minimum value of ‖A − λI‖. We derive some results concerning the location of St(A) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal A its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St(A)=0 and Roberts orthogonality of A to the identity operator are established.

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KW - Roberts orthogonality

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ER -

ON THE STAMPFLI POINT OF SOME OPERATORS AND MATRICES

Abstract

Keywords

ASJC Scopus subject areas

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