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

2025/10/28 by Kuzma, Bojan, Stefanović, Srdjan, Tanaka, Ryotaro
#46B20 #46B80 #47B49 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 46L35

paper · doi:10.48550/arxiv.2510.24308

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.

Citations

• Isomorphisms of Birkhoff-James orthogonality on finite-dimensional C^*-algebra
• Birkhoff-James classification of finite-dimensional C^*-algebras
• Non-linear classification of finite-dimensional simple C^*-algebras
• Isolated vertices and diameter of the BJ-orthograph in C^*-algebras
• What does Birkhoff-James orthogonality know about the norm?
• What does Birkhoff--James orthogonality know about the norm?
• On Birkhoff-James orthogonality preservers between real non-isometric Banach spaces
• Approximately invertible elements in non-unital normed algebras
• Transformations preserving the norm of means between positive cones of general and commutative C^*-algebras
• Quantum Rényi relative entropies on density spaces of C^*-algebras: their symmetries and their essential difference
• Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces
• A new proof of the noncommutative Banach-Stone theorem
• Operators preserving orthogonality are isometries

Cited by

• C*-submodule preserving module mappings on Hilbert C*-modules

Related

• Birkhoff-James classification of finite-dimensional C^*-algebras
• Isomorphisms of Birkhoff-James orthogonality on finite-dimensional C^*-algebra
• On relationship among three types of Birkhoff-James orthogonality
• A generalized Birkhoff-James orthogonality and norm parallelism in unital C^*-algebras and their characterizations
• Classification of abelian finite-dimensional C^*-algebras by orthogonality