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 F n 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.
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Oudghiri, M. Weyl’s Theorem and Perturbations. Integr. equ. oper. theory 53, 535–545 (2005). https://doi.org/10.1007/s00020-004-1342-4
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DOI: https://doi.org/10.1007/s00020-004-1342-4