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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Jordan $ *$-derivations of standard operator algebras


Author: Peter Šemrl
Journal: Proc. Amer. Math. Soc. 120 (1994), 515-518
MSC: Primary 46L57; Secondary 46L70, 47B48, 47D25
MathSciNet review: 1186136
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Abstract: Let $ H$ be a real or complex Hilbert space, $ \dim H > 1$, and $ \mathcal{B}(H)$ the algebra of all bounded linear operators on $ H$. Assume that $ \mathcal{A}$ is a standard operator algebra on $ H$. Then every additive Jordan $ {\ast}$-derivation $ J:\mathcal{A} \to \mathcal{B}(H)$ is of the form $ J(A) = AT - T{A^{\ast}}$ for some $ T \in \mathcal{B}(H)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186136-6
PII: S 0002-9939(1994)1186136-6
Article copyright: © Copyright 1994 American Mathematical Society