B-fredholm and spectral properties for multipliers in Banach algebras

摘要

The main purpose of this paper is to study spectral and B-Fredholm properties of a multiplierT acting on a semi-simple regular tauberian commutative Banach algebraA. We show thatT is a B-Fredholm operator if and only ifT is a semi B-Fredholm operator, and in this case we have the indexind(T)=0. Moreover we give some spectral properties for multipliers. Spectral mapping theorems for the Weyl’s and B-Weyl spectrum of a multiplier are also considered. Furthermore we show that Weyl’s theorem and generalized Weyl’s theorem hold for a multiplierT. Finally we give sufficient conditions for a multiplier to be a product of an invertible and an idempotent operators.