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Transactions of the American Mathematical Society

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A note on limits of unitarily equivalent operators


Author: Lawrence A. Fialkow
Journal: Trans. Amer. Math. Soc. 232 (1977), 205-220
MSC: Primary 47A65
DOI: https://doi.org/10.1090/S0002-9947-1977-0448131-6
MathSciNet review: 0448131
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Abstract: Let $ \mathcal{U}(\mathcal{H})$ denote the set of all unitary operators on a separable complex Hilbert space $ \mathcal{H}$. If T is a bounded linear operator on $ \mathcal{H}$, let $ {\pi _T}$ denote the mapping of $ \mathcal{U}(\mathcal{H})$ onto $ \mathcal{U}(T)$ given by conjugation. It is proved that if T is normal or isometric, then there exists a locally defined continuous cross-section for $ {\pi _T}$ if and only if the spectrum of T is finite. Examples of nonnormal operators with local cross-sections are given.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0448131-6
Article copyright: © Copyright 1977 American Mathematical Society

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