Some remarks on the Volterra operator

Foiaş, Ciprian; Williams, J. P.

doi:10.1090/S0002-9939-1972-0295126-2

Some remarks on the Volterra operator
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by Ciprian Foiaş and J. P. Williams

Proc. Amer. Math. Soc. 31 (1972), 177-184

DOI: https://doi.org/10.1090/S0002-9939-1972-0295126-2

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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 $|z| \leqq ||T||$ 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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