Weyl type theorems and class \(A(s,t)\) operators. (English) Zbl 1244.47017

Rashid, Mohammad H. M.; Zguitti, Hassane

Math. Inequal. Appl. 14, No. 3, 581-594 (2011).

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 \(( \beta )\).

Reviewer: Mohammed Hichem Mortad (Oran)

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

Keywords:

single valued extension property; Weyl theorem; class \(wA(s, t)\); class \(A(s, t)\)