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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0295114-0
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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DOI: https://doi.org/10.1090/S0002-9947-1972-0295114-0
Keywords: Operator, Hilbert space, resolvent, characteristic function, spectral set, similarity, spectral type operator
Article copyright: © Copyright 1972 American Mathematical Society