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Proceedings of the American Mathematical Society

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Norm conditions on resolvents of similarities of Hilbert space operators and applications to direct sums and integrals of operators


Author: Frank Gilfeather
Journal: Proc. Amer. Math. Soc. 68 (1978), 44-48
MSC: Primary 47A10; Secondary 47A60
DOI: https://doi.org/10.1090/S0002-9939-1978-0475583-4
MathSciNet review: 475583
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Abstract: Similarities of an operator T are determined so that on certain sets the norm of the resolvents of the similarity satisfy bounding conditions independent of T. The results are applied to show that direct sums and integrals of operators are quasi-similar to operators with spectrum depending only on the spectrum of the summands.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0475583-4
Article copyright: © Copyright 1978 American Mathematical Society

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