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Weyl’s Theorem and Perturbations

Research paper by Mourad Oudghiri

Indexed on: 16 Aug '05Published on: 16 Aug '05Published in: Integral Equations and Operator Theory



Abstract

In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fn is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results for this class.