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Perturbations and Weyl's theorem

Author: B. P. Duggal
Journal: Proc. Amer. Math. Soc. 135 (2007), 2899-2905
MSC (2000): Primary 47A10, 47A12, 47B20
Published electronically: May 8, 2007
MathSciNet review: 2317967
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Abstract | References | Similar Articles | Additional Information

Abstract: A Banach space operator $ T$ is completely hereditarily normaloid, $ T\in\mathcal{CHN}$, if either every part, and (also) $ T_p^{-1}$ for every invertible part $ T_p$, of $ T$ is normaloid or if for every complex number $ \lambda$ every part of $ T-\lambda I$ is normaloid. Sufficient conditions for the perturbation $ T+A$ of $ T\in\mathcal{CHN}$ by an algebraic operator $ A$ to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator $ (T+A)^*$ satisfies $ a$-Weyl's theorem.

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Additional Information

B. P. Duggal
Affiliation: 8 Redwood Grove, Northfield Avenue, London W5 4SZ, England, United Kingdom

Keywords: Banach space, $\mathcal{CHN}$-operator, algebraic operator, perturbation, Weyl's theorem
Received by editor(s): February 4, 2006
Received by editor(s) in revised form: June 1, 2006
Published electronically: May 8, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society

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