PROF. NZIMBI BERNARD MUTUKU

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.

We discuss basic properties of Analysis and synthesis operators a frame. The structure of matrix
representation of the Synthesis operator is also analysed. This matrix is what most frame constructions in
fact focus on. The frame operator which is just the joining together of the analysis and synthesis
operators is fundamental for the reconstruction of signals from frame coefficients

In this paper we introduce the notions of an A-self-adjoint, an A-skewadjoint linear operator, where A is a self-adjoint and invertible operator and related classes of operators, which generalize some known classes of operators. We investigate some properties of these operators and show that these operators share some properties with some known classes of operators. We prove some results on some equivalence of these operators and investigate conditions under which these operators are self-adjoint, unitary, skew-adjoint, normal, hyponormal, quasinormal or binormal. We also attempt to locate the spectra of such operators