Inclusion regions for numerical ranges and linear preservers

C. K. Li; Nung Sing Sze

doi:10.1080/03081080310001614275

Inclusion regions for numerical ranges and linear preservers

C. K. Li
, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

Let R be a proper subset of the complex plane, and let SRbe the set of n × n complex matrices A such that the numerical range W(A) satisfies W(A) ⊆ R. Linear maps φ on matrices satisfying φ(SR) = SRare characterized. Denote by S̃Rthe set of n × n complex matrices A such that the numerical radius r(A) satisfies r(A) ⊆ R for a proper subset R of nonnegative real numbers. Linear maps φ on matrices satisfying φ(S̃R) = S̃Rare also characterized. Analogous results on Hermitian matrices are obtained.

Original language	English
Pages (from-to)	235-249
Number of pages	15
Journal	Linear and Multilinear Algebra
Volume	52
Issue number	3-4
DOIs	https://doi.org/10.1080/03081080310001614275
Publication status	Published - 1 Jan 2004
Externally published	Yes

Keywords

Hermitian matrices
Linear maps
Numerical range (radius)

ASJC Scopus subject areas

Algebra and Number Theory

More information

10.1080/03081080310001614275

Cite this

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AU - Sze, Nung Sing

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N2 - Let R be a proper subset of the complex plane, and let SRbe the set of n × n complex matrices A such that the numerical range W(A) satisfies W(A) ⊆ R. Linear maps φ on matrices satisfying φ(SR) = SRare characterized. Denote by S̃Rthe set of n × n complex matrices A such that the numerical radius r(A) satisfies r(A) ⊆ R for a proper subset R of nonnegative real numbers. Linear maps φ on matrices satisfying φ(S̃R) = S̃Rare also characterized. Analogous results on Hermitian matrices are obtained.

AB - Let R be a proper subset of the complex plane, and let SRbe the set of n × n complex matrices A such that the numerical range W(A) satisfies W(A) ⊆ R. Linear maps φ on matrices satisfying φ(SR) = SRare characterized. Denote by S̃Rthe set of n × n complex matrices A such that the numerical radius r(A) satisfies r(A) ⊆ R for a proper subset R of nonnegative real numbers. Linear maps φ on matrices satisfying φ(S̃R) = S̃Rare also characterized. Analogous results on Hermitian matrices are obtained.

KW - Hermitian matrices

KW - Linear maps

KW - Numerical range (radius)

UR - https://www.scopus.com/pages/publications/2442473961

U2 - 10.1080/03081080310001614275

DO - 10.1080/03081080310001614275

M3 - Journal article

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VL - 52

SP - 235

EP - 249

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 3-4

ER -

Inclusion regions for numerical ranges and linear preservers

Abstract

Keywords

ASJC Scopus subject areas

More information

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