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arXiv · 2510.24308

On preservers of strong Birkhoff-James orthogonality between $C^*$-algebras

Bojan Kuzma·Srdjan Stefanović·Ryotaro Tanaka
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Abstract

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of (possibly nonlinear) strong Birkhoff-James isomorphisms between compact $C^*$-algebras are determined. A nonlinear characterization of compact $C^*$-algebras in terms of strong Birkhoff-James orthogonality is also given.

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Bojan Kuzma, Srdjan Stefanović, Ryotaro Tanaka. 2025-10-28. On preservers of strong Birkhoff-James orthogonality between $C^*$-algebras. https://arxiv.org/abs/2510.24308

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