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Some remarks on the Volterra operator


Authors: Ciprian Foiaş and J. P. Williams
Journal: Proc. Amer. Math. Soc. 31 (1972), 177-184
MSC: Primary 47B99
MathSciNet review: 0295126
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Abstract: By considering various functions of the Volterra operator $ V$, examples are obtained to show that (i) similar contractions need not have the same defect numbers, (ii) unicellular operators may have large spectra, and (iii) the disk $ \vert z\vert \leqq \vert\vert T\vert\vert$ need not be a minimal spectral set for an operator $ T$ of the form 1 + compact. A complete description is also given of those disks that are a spectral set for some conjugate of $ V$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295126-2
Keywords: Similarity, numerical range, spectral sets, unicellular operators, theory of contractions
Article copyright: © Copyright 1972 American Mathematical Society