Characterization of B-Fredholm Quotient Operator with Application to Strict Quasi-normal Contractions

In this paper, we give a characterization of a B-Fredholm quotient of two bounded linear operators A and M satisfying certain conditions on a Hilbert space. We derive also the relationships between some B-Fredholm spectra of the linear operator pencil λ M-A, where λ\in\mathbb{C}, and those of the quotient of A and M. These results are finally applied to a closed densely defined linear operator T=Γ(C)=C/(I-C * C) ½ , where C a pure quasi-normal contraction and the symbol I the identity operator, by giving a B-Fredholm correspondence between T and C, and some related results concerning B-Weyl operators and Drazin invertible ones.