Open Access
December, 2019 Isometries on Positive Definite Operators with Unit Fuglede-Kadison Determinant
Marcell Gaál, Gergő Nagy, Patricia Szokol
Taiwanese J. Math. 23(6): 1423-1433 (December, 2019). DOI: 10.11650/tjm/190205


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.


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Marcell Gaál. Gergő Nagy. Patricia Szokol. "Isometries on Positive Definite Operators with Unit Fuglede-Kadison Determinant." Taiwanese J. Math. 23 (6) 1423 - 1433, December, 2019.


Received: 17 October 2018; Revised: 22 February 2019; Accepted: 25 February 2019; Published: December, 2019
First available in Project Euclid: 8 March 2019

zbMATH: 07142980
MathSciNet: MR4033552
Digital Object Identifier: 10.11650/tjm/190205

Primary: 46L40
Secondary: 47L30

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

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

Vol.23 • No. 6 • December, 2019
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