Search results for "Weyl’s theorems"

Property (w) for perturbations of polaroid operators

2008

Abstract A bounded linear operator T ∈ L ( X ) acting on a Banach space 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-point spectrum σ wa ( T ) is 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 polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.