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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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