Taiwanese Journal of Mathematics

Isometries on Positive Definite Operators with Unit Fuglede-Kadison Determinant

Marcell Gaál, Gergő Nagy, and Patricia Szokol

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Abstract

In this paper we explore the structure of certain surjective generalized isometries (which are transformations that leave any given member of a large class of generalized distance measures invariant) of the set of positive invertible elements in a finite von Neumann factor with unit Fuglede-Kadison determinant. We conclude that any such map originates from either an algebra $^*$-isomorphism or an algebra $^*$-antiisomorphism of the underlying operator algebra.

Article information

Source
Taiwanese J. Math., Volume 23, Number 6 (2019), 1423-1433.

Dates
Received: 17 October 2018
Revised: 22 February 2019
Accepted: 25 February 2019
First available in Project Euclid: 8 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1552013881

Digital Object Identifier
doi:10.11650/tjm/190205

Mathematical Reviews number (MathSciNet)
MR4033552

Zentralblatt MATH identifier
07142980

Subjects
Primary: 46L40: Automorphisms
Secondary: 47L30: Abstract operator algebras on Hilbert spaces

Keywords
isometries von Neumann algebras positive definite operators Fuglede-Kadison determinant totally geodesic submanifolds

Citation

Gaál, Marcell; Nagy, Gergő; Szokol, Patricia. Isometries on Positive Definite Operators with Unit Fuglede-Kadison Determinant. Taiwanese J. Math. 23 (2019), no. 6, 1423--1433. doi:10.11650/tjm/190205. https://projecteuclid.org/euclid.twjm/1552013881


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