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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the local spectra of seminormal operators


Author: Kevin F. Clancey
Journal: Proc. Amer. Math. Soc. 72 (1978), 473-479
MSC: Primary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1978-0509237-2
MathSciNet review: 509237
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0509237-2
Article copyright: © Copyright 1978 American Mathematical Society