Isometries on Noncommutative Symmetric Spaces

Let 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 . Let be a separable symmetric space of τ-measurable operators, whose norm is not pro...

Full description

Saved in:
Bibliographic Details
Published in:Doklady. Mathematics 2021, Vol.103 (1), p.54-56
Main Authors: Sukochev, F. A., Huang, J.
Format: Article
Language:English
Subjects:
Hilbert space
Mathematics
Mathematics and Statistics
Operators (mathematics)
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let 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 . Let be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅|| 2 on . We provide a description of all bounded Hermitian operators on and all surjective linear isometries of this space.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562421010129