Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Derivations, homomorphisms, and operator ideals

Author: T. B. Hoover
Journal: Proc. Amer. Math. Soc. 62 (1977), 293-298
MSC: Primary 46L05
MathSciNet review: 0435860
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Abstract: Let $ \mathfrak{A}$ be a $ {C^\ast}$-algebra of operators on a Hilbert space, and let $ {C_p}$ be the Schatten p-ideal. It is shown that every derivation from $ \mathfrak{A}$ to $ {C_p}$ is inner. A similar argument shows that two $ {C^\ast}$-homomorphisms which agree modulo $ {C_p}$ are equivalent.

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Keywords: Derivation, $ {C^\ast}$-homomorphism, operator ideals
Article copyright: © Copyright 1977 American Mathematical Society