A quantitative version of Herstein's theorem for Jordan *-isomorphisms (CROSBI ID 224302)
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Podaci o odgovornosti
Ilišević, Dijana ; Turnšek, Aleksej
engleski
A quantitative version of Herstein's theorem for Jordan *-isomorphisms
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.
stability ; Jordan *-isomorphism ; C*-algebra
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Podaci o izdanju
64 (2)
2016.
156-168
objavljeno
0308-1087
1563-5139
10.1080/03081087.2015.1028169