
doi: 10.1007/bf02874778
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.
Linear operators on Banach algebras, Perturbation theory of linear operators, Weyl's theorem, \(B\)-Fredholm operators, multipliers, General theory of topological algebras, (Semi-) Fredholm operators; index theories, Spectrum, resolvent, Banach algebras, generalized Weyl's theorem
Linear operators on Banach algebras, Perturbation theory of linear operators, Weyl's theorem, \(B\)-Fredholm operators, multipliers, General theory of topological algebras, (Semi-) Fredholm operators; index theories, Spectrum, resolvent, Banach algebras, generalized Weyl's theorem
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