Isometries on Noncommutative Symmetric Spaces

F. A. Sukochev; J. Huang

doi:10.1134/S1064562421010129

Isometries on Noncommutative Symmetric Spaces

F. A. Sukochev^*
, J. Huang^*

^*Corresponding author for this work

University of New South Wales
North Ossetian State University

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

Abstract

Abstract: Let M be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space H. Let E(M, τ) be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅||₂ on L₂(M, τ). We provide a description of all bounded Hermitian operators on E(M, τ) and all surjective linear isometries of this space.

Original language	English
Pages (from-to)	54-56
Number of pages	3
Journal	Doklady Mathematics
Volume	103
Issue number	1
DOIs	https://doi.org/10.1134/S1064562421010129
State	Published - Jan 2021
Externally published	Yes

Keywords

Hermitian operators
semifinite von Neumann algebra
surjective isometries
symmetric spaces

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10.1134/S1064562421010129

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abstract = "Abstract: Let M be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space H. Let E(M, τ) be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅||2 on L2(M, τ). We provide a description of all bounded Hermitian operators on E(M, τ) and all surjective linear isometries of this space.",

keywords = "Hermitian operators, semifinite von Neumann algebra, surjective isometries, symmetric spaces",

author = "Sukochev, \{F. A.\} and J. Huang",

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year = "2021",

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doi = "10.1134/S1064562421010129",

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N2 - Abstract: Let M be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space H. Let E(M, τ) be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅||2 on L2(M, τ). We provide a description of all bounded Hermitian operators on E(M, τ) and all surjective linear isometries of this space.

AB - Abstract: Let M be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space H. Let E(M, τ) be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅||2 on L2(M, τ). We provide a description of all bounded Hermitian operators on E(M, τ) and all surjective linear isometries of this space.

KW - Hermitian operators

KW - semifinite von Neumann algebra

KW - surjective isometries

KW - symmetric spaces

UR - https://www.scopus.com/pages/publications/85105491837

U2 - 10.1134/S1064562421010129

DO - 10.1134/S1064562421010129

M3 - 文章

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SN - 1064-5624

VL - 103

SP - 54

EP - 56

JO - Doklady Mathematics

JF - Doklady Mathematics

IS - 1

ER -

Isometries on Noncommutative Symmetric Spaces

Abstract

Keywords

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