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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A local spectral theory for operators. III. Resolvents, spectral sets and similarity

Author: J. G. Stampfli
Journal: Trans. Amer. Math. Soc. 168 (1972), 133-151
MSC: Primary 47A25
MathSciNet review: 0295114
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Abstract: Let $T$ be a bounded linear operator on a Hilbert space and assume $T$ has thin spectrum. When is $T$ similar to a normal operator? This problem is studied in a variety of situations and sufficient conditions are given in terms of characteristic functions, resolvents, spectral sets, and spectral resolutions. By contrast, the question “When is $T$ normal?” has a relatively simple answer since in that case a necessary and sufficient condition can be given in terms of the resolvent alone.

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Keywords: Operator, Hilbert space, resolvent, characteristic function, spectral set, similarity, spectral type operator
Article copyright: © Copyright 1972 American Mathematical Society