Further common local spectral properties for bounded linear operators

Abstract

We study common local spectral properties for bounded linear operators A ∈ ℒ(X,Y) and B,C ∈ ℒ (Y,X) such that A(BA)2=ABACA=ACABA=(AC)2A. We prove that AC and BA share the single valued extension property, the Bishop property (β), the property (β e), the decomposition property (δ) and decomposability. Closedness of analytic core and quasinilpotent part are also investigated. Some applications to Fredholm operators are given.