Weyl's Type Theorems for Quasi-Class A Operators

M H M Rashid ,Mohd Salmi Md Noorani ,A S Saari

doi:10.3844/jmssp.2008.70.74

Abstract

A variant of Weyl theorem for a class of quasi-class A acting on an infinite complex Hilbert space were discussed. If the adjoint of T is a quasi-class A operator, then the generalized a-Weyl holds for f(T) , for every function that analytic on the spectrum of T. The generalized Weyl theorem holds for a quasi-class A was proved. Also, a characterization of the Hilbert space as a direct sum of range and kernel of a quasi-class A was given. Among other things, if the operator is a quasi-class A, then the B-Weyl spectrum satisfies the spectral theorem was characterized.

Highlights

Throughout this study let B(H) and K(H), denote, respectively, the algebra of bounded linear operators and the ideal of compact operators acting on an infinite dimensional separable Hilbert space H
Two other important classes of operators in Fredholm theory are the class of all upper semi-Browder operators
The theorem shows that for quasi-class A operators the spectral mapping theorem holds for the essential approximate point spectrum

Summary

Introduction

Throughout this study let B(H) and K(H), denote, respectively, the algebra of bounded linear operators and the ideal of compact operators acting on an infinite dimensional separable Hilbert space H. The class of all Weyl Operators W(H) is defined by In [8] , the authors proved that Weyl’s theorem holds for quasi-classA, in this paper, we prove that generalized Weyl's holds for quasi-class A operators.

Results

Conclusion