Abstract
A bounded linear operator T ∈ L ( X ) defined on a Banach space X satisfies property ( w ) , a variant of Weyl's theorem, if the complement in the approximate point spectrum σ a ( T ) of the Weyl essential approximate spectrum σ wa ( T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property ( w ) , for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T.
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