A local spectral theory for operators. III. Resolvents, spectral sets and similarity
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- by J. G. Stampfli
- Trans. Amer. Math. Soc. 168 (1972), 133-151
- DOI: https://doi.org/10.1090/S0002-9947-1972-0295114-0
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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.References
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Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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