\(B\)-Fredholm and spectral properties for multipliers in Banach algebras (Q996945)

The paper studies spectral and \(B\)-Fredholm properties of multipliers acting on semi-simple regular Tauberian commutative Banach algebras. It is shown that a multiplier is \(B\)-Fredholm if and only if it is semi \(B\)-Fredholm, and in this case the index of \(T\) is zero. Spectral mapping theorems for the Weyl and \(B\)-Weyl spectrum are proven, and it is shown that the Weyl theorem and the generalized Weyl theorem hold for multipliers. Finally, sufficient conditions are given for a multiplier to be the product of an invertible and an idempotent operator.