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Proceedings of the American Mathematical Society

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

 

 

On compact operators in the weak closure of the range of a derivation


Author: Hong W. Kim
Journal: Proc. Amer. Math. Soc. 40 (1973), 482-486
MSC: Primary 47B47; Secondary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1973-0318956-8
MathSciNet review: 0318956
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Abstract: It is shown that if $ K$ is a compact operator which commutes with a bounded operator $ A$ on a Hilbert space $ H$ and if $ K$ is contained in the weak closure of the range of the derivation induced by $ A$, then $ K$ is quasinilpotent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318956-8
Keywords: Range of a derivation, eigenvalues, quasinilpotent operators, norm closure, weak operator topology, commutant of an operator, compact operator
Article copyright: © Copyright 1973 American Mathematical Society