Naslov
A quantitative version of Herstein's theorem for Jordan *-isomorphisms

Autori
Ilišević, Dijana ; Turnšek, Aleksej

Izvornik
Linear and multilinear algebra (0308-1087) 64 (2016), 2; 156-168

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
stability ; Jordan *-isomorphism ; C*-algebra

Sažetak
We study linear mappings between C*-algebras A and B, which approximately satisfy Jordan multiplicativity condition and a *-preserving condition (that is, the so-called \epsilon-approximate Jordan *-homomorphisms). We first prove that every such a mapping is automatically continuous and we give the estimates of its norm, as well as the estimates of the norm of its inverse if it is bijective. If K(H_1) \subseteq A \subseteq B(H_1), K(H_2) \subseteq B \subseteq B(H_2), and \psi : A \to B is a bijective \epsilon-approximate Jordan *-homomorphism with sufficiently small \epsilon > 0, then either \psi^{; ; ; -1}; ; ; has a large norm, or \psi is close to a Jordan *-isomorphism, that is, to a mapping of the form X \mapsto UXU*, or X \mapsto UX^tU*, for some unitary U \in B(H_1, H_2). We also give the corresponding quantitative estimate.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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