Weyl’s Theorems for Some Classes of Operators

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We introduce the class of operators on Banach spaces having prop- erty (H) and study Weyl's theorems, and related results for operators which satisfy this property. We show that a- Weyl's theorem holds for every decom- posable operator having property (H). We also show that a-Weyl's theorem holds for every multiplier T of a commutative semi-simple regular Taube- rian Banach algebra. In particular every convolution operator Tµ of a group algebra L 1 (G), G a locally compact abelian group, satisfies a-Weyl's theo- rem. Similar results are given for multipliers of other important commutative Banach algebras.