Polaroid operators satisfying Weyl’s theorem

Abstract

A Banach space operator T is polaroid and satisfies Weyl’s theorem if and only if T is Kato type at points λ ∈ iso σ( T) and has SVEP at points λ not in the Weyl spectrum of T. For such operators T, f( T) satisfies Weyl’s theorem for every non-constant function f analytic on a neighborhood of σ( T) if and only if f( T ∗) satisfies Weyl’s theorem.