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Extending surjective maps preserving the norm of symmetric Kubo-Ando means

Part of: Selfadjoint operator algebras General theory of linear operators Special classes of linear operators

Published online by Cambridge University Press:  30 January 2025

Emmanuel Chetcuti  and
Curt Healey
Emmanuel Chetcuti
Affiliation:
Department of Mathematics, Faculty of Science, University of Malta, Msida, MSD 2080, Malta emanuel.chetcuti@um.edu.mt
Curt Healey*
Affiliation:
Department of Mathematics, Faculty of Science, University of Malta, Msida, MSD 2080, Malta emanuel.chetcuti@um.edu.mt
*
e-mail: curt.c.healey.13@um.edu.mt
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Abstract

In Dong et al. (2022, Journal of Operator Theory 88, 365–406), the authors addressed the question of whether surjective maps preserving the norm of a symmetric Kubo-Ando mean can be extended to Jordan $\ast $-isomorphisms. The question was affirmatively answered for surjective maps between the positive definite cones of unital $C^{*}$-algebras for certain specific classes of symmetric Kubo-Ando means. Here, we give a comprehensive answer to this question for surjective maps between the positive definite cones of $AW^{*}$-algebras preserving the norm of any symmetric Kubo-Ando mean.

Keywords

Kubo-Ando connectionC*-algebraAW*-algebrapositive definite conepreservers

MSC classification

Primary: 47A64: Operator means, shorted operators, etc. 47B49: Transformers, preservers (operators on spaces of operators) 46L40: Automorphisms
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 10
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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