Extending surjective maps preserving the norm of symmetric kubo-ando means

TL;DR

This paper investigates whether surjective maps that preserve the norm of symmetric Kubo-Ando means can be extended to Jordan *-isomorphisms, providing a comprehensive answer for $AW^{*}$-algebras.

Contribution

It extends previous results by establishing a general theorem for surjective maps preserving the norm of any symmetric Kubo-Ando mean on $AW^{*}$-algebras.

Findings

Surjective maps preserving the norm of symmetric Kubo-Ando means extend to Jordan *-isomorphisms.

The result applies to all symmetric Kubo-Ando means on $AW^{*}$-algebras.

Provides a unified framework for understanding norm-preserving maps in operator algebra theory.

Abstract

Recently, the question of whether surjective maps preserving the norm of a symmetric Kubo-Ando mean can be extended to Jordan $\ast$-isomorphisms has been tackled. The question was affirmatively answered for surjective maps between $C^{*}$-algebras for certain specific classes of symmetric Kubo-Ando means. Here, we give a comprehensive answer to this question for surjective maps between $AW^{*}$-algebras preserving the norm of any symmetric Kubo-Ando mean.