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Extending surjective maps preserving the norm of symmetric Kubo-Ando means
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 30 January 2025, pp. 1-10
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- Article
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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.
