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Weyl type theorems and class $$A(s,t)$$ operators. (English) Zbl 1244.47017
Let $$T$$ be a linear operator belonging to the class $$A(s,t)$$, where $$0<s,t\leq 1$$. Let $$f$$ be an analytic function on an open neighborhood of the spectrum of $$T$$. In this paper, the authors show that Weyl’s and generalized Weyl’s theorems do hold for $$f(T)$$. They also prove that $$A(s,t)$$ verifies Bishop’s property $$( \beta )$$.

MSC:
 47A55 Perturbation theory of linear operators 47A53 (Semi-) Fredholm operators; index theories 47B20 Subnormal operators, hyponormal operators, etc. 47A10 Spectrum, resolvent 47A11 Local spectral properties of linear operators
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