Weyl's theorem for algebraically totally hereditarily normaloid operators |
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Authors: | B.P. Duggal |
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Affiliation: | 8 Redwood Grove, Ealing, London W5 4SZ, England, UK |
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Abstract: | A Banach space operator T∈B(X) is said to be totally hereditarily normaloid, T∈THN, if every part of T is normaloid and every invertible part of T has a normaloid inverse. The operator T is said to be an H(q) operator for some integer q?1, T∈H(q), if the quasi-nilpotent part H0(T−λ)=(T−λ)−q(0) for every complex number λ. It is proved that if T is algebraically H(q), or T is algebraically THN and X is separable, then f(T) satisfies Weyl's theorem for every function f analytic in an open neighborhood of σ(T), and T∗ satisfies a-Weyl's theorem. If also T∗ has the single valued extension property, then f(T) satisfies a-Weyl's theorem for every analytic function f which is non-constant on the connected components of the open neighborhood of σ(T) on which it is defined. |
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Keywords: | Weyl's theorems Single valued extension property THN operators |
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