Property \((UW_\Pi )\) holds for a bounded linear operator \(T \in B(X),\) defined on a complex infinite dimensional Banach space X, if the poles of the resolvent of T are exactly the spectral points \(\lambda \) for which \(\lambda I-T\) is upper semi-Weyl. In this paper, we discuss the relationship between property \((UW_\Pi )\) and other Weyl type theorems. The stability of property \((UW_\Pi )\) is also studied under nilpotent, quasi-nilpotent, finite-dimensional or compact perturbations commuting with T.
Property \((UW_\Pi )\)Weyl type theorems SVEP perturbation theory
Mathematics Subject Classification
Primary 47A10 47A11 Secondary 47A53 47A55
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The authors are grateful to the referees for their valuable comments and suggestions.
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