Pseudo B-Fredholm Operators and Spectral Theory

TL;DR

This paper explores the properties of pseudo B-Fredholm operators, establishing their equivalence to pseudo Fredholm operators and analyzing spectral conditions related to their spectra.

Contribution

It proves the equivalence of pseudo B-Fredholm and pseudo Fredholm operators and characterizes spectral emptiness conditions for these operators.

Findings

Pseudo B-Fredholm operators are shown to be pseudo Fredholm operators.

The pseudo B-Weyl spectrum is empty if and only if the pseudo B-Fredholm spectrum is empty.

Study of symmetric differences between parts of the spectrum.

Abstract

In this paper, we show that every pseudo B-Fredholm operator is a pseudo Fredholm operator. Afterwards, we prove that the pseudo B-Weyl spectrum is empty if and only if the pseudo B-Fredholm spectrum is empty. Also, we study a symmetric difference between some parts of the spectrum.