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


On the essential numerical range of a generalized derivation

Author: Bojan Magajna
Journal: Proc. Amer. Math. Soc. 99 (1987), 86-92
MSC: Primary 47B47; Secondary 47A12
MathSciNet review: 866435
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Abstract: Let $ A$ and $ B$ be bounded operators on Hilbert spaces $ \mathcal{H}$ and $ \mathcal{L}$, respectively. The essential numerical range of the operator $ X \to AX - XB$, defined on the Hilbert-Schmidt class $ {\mathcal{C}^2}\left( {\mathcal{L},\mathcal{H}} \right)$ is expressed in terms of the numerical and the essential numerical ranges of $ A$ and $ B$.

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PII: S 0002-9939(1987)0866435-1
Keywords: Generalized derivations, essential numerical range, Hilbert-Schmidt class
Article copyright: © Copyright 1987 American Mathematical Society