On the local spectra of seminormal operators

Clancey, Kevin F.

doi:10.1090/S0002-9939-1978-0509237-2

On the local spectra of seminormal operators
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by Kevin F. Clancey

Proc. Amer. Math. Soc. 72 (1978), 473-479

DOI: https://doi.org/10.1090/S0002-9939-1978-0509237-2

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Abstract:

Two theorems on the local spectra of seminormal operators are deduced. In the first theorem it is shown that when T is hyponormal any solution of the equation $(T - \lambda )x(\lambda ) = x$ on an open set in the plane is necessarily analytic. The second theorem establishes the existence of vectors with small local spectra for a cohyponormal operator with a finite rank self-commutator.

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