Perturbations and Weyl’s theorem

Duggal, B.

doi:10.1090/S0002-9939-07-08799-0

Perturbations and Weyl’s theorem
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by B. P. Duggal PDF

Proc. Amer. Math. Soc. 135 (2007), 2899-2905 Request permission

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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