Preservers for norms of Lie product

Chi Kwong Li; Edward Poon; Nung Sing Sze

doi:10.7153/oam-03-10

Preservers for norms of Lie product

Chi Kwong Li, Edward Poon, Nung Sing Sze

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

20 Citations (Scopus)

Abstract

Let {double pipe} · {double pipe} be a unitary similarity invariant norm on the set Mn of n × n complex matrices. A description is obtained for surjective maps φ on Mnsatisfying {double pipe}AB - BA{double pipe} = {double pipe}φ (A)φ (B)-φ (B)φ (A){double pipe} for all A,B ∈ Mn. The general theorem covers the special cases when the norm is one of the Schatten p-norms, the Ky-Fan k-norms, or the k-numerical radii.

Original language	English
Pages (from-to)	187-203
Number of pages	17
Journal	Operators and Matrices
Volume	3
Issue number	2
DOIs	https://doi.org/10.7153/oam-03-10
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Lie product
Unitarily invariant and unitary similarity invariant norms

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

More information

10.7153/oam-03-10

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abstract = "Let {double pipe} · {double pipe} be a unitary similarity invariant norm on the set Mn of n × n complex matrices. A description is obtained for surjective maps φ on Mnsatisfying {double pipe}AB - BA{double pipe} = {double pipe}φ (A)φ (B)-φ (B)φ (A){double pipe} for all A,B ∈ Mn. The general theorem covers the special cases when the norm is one of the Schatten p-norms, the Ky-Fan k-norms, or the k-numerical radii.",

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AU - Sze, Nung Sing

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N2 - Let {double pipe} · {double pipe} be a unitary similarity invariant norm on the set Mn of n × n complex matrices. A description is obtained for surjective maps φ on Mnsatisfying {double pipe}AB - BA{double pipe} = {double pipe}φ (A)φ (B)-φ (B)φ (A){double pipe} for all A,B ∈ Mn. The general theorem covers the special cases when the norm is one of the Schatten p-norms, the Ky-Fan k-norms, or the k-numerical radii.

AB - Let {double pipe} · {double pipe} be a unitary similarity invariant norm on the set Mn of n × n complex matrices. A description is obtained for surjective maps φ on Mnsatisfying {double pipe}AB - BA{double pipe} = {double pipe}φ (A)φ (B)-φ (B)φ (A){double pipe} for all A,B ∈ Mn. The general theorem covers the special cases when the norm is one of the Schatten p-norms, the Ky-Fan k-norms, or the k-numerical radii.

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KW - Unitarily invariant and unitary similarity invariant norms

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ER -

Preservers for norms of Lie product

Abstract

Keywords

ASJC Scopus subject areas

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