Weyl and Browder theorems for operators with or without SVEP at zero

Abstract

The study of operators having some special spectral properties like Weyl's theorem, Browder's theorem and the SVEP has been of important interest for some time now. The SVEP is very useful in the study of the local spectral theory. In this paper, we explore the single-valued extension property (SVEP) for some operators on Hilbert spaces. We characterize operators with or without SVEP at zero and those where Weyl's and Browder's theorems hold. It is shown that if a Fredholm operator has no SVEP at zero, then zero is an accumulation point of the spectrum of the operator. It is also shown that quasi similar Fredholm operators have equal Weyl spectrum.