Symmetric Difference Between Pseudo B-Fredholm Spectrum and Spectra Originated from Fredholm Theory

Abstract

In this paper, we continue the study of Pseudo B-Fredholm operators introduced
in E. Boasso, isolated spectral points and Koliha-Drazin invertible elements in quotient Banach
algebras and homomorphism ranges, Mathematical Proceding of the Royal Irich Academy Vol. 115A, No. 2(2015), pp.1-15.
We prove that every pseudo B-Fredholm operator is a pseudo Fredholm operator. Afterwards,
we prove that the pseudo B-Weyl spectrum introduced in
H. Zariouh, H. Zguitti, on pseudo B-Weyl operators and generalized drazin invertible for operator matrices, Linear and Multilinear Algebra, Vol 64, Issue 7, (2016), 1245-1257; is empty if and only if the pseudo B-Fredholm spectrum is empty. Also,
we study a symmetric difference between the pseud B-Fredholm spectrum and others parts of the spectrum.