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functional analysis

Quasi-Fredholm spectrum and compact perturbations

arXiv:1908.04105

summary

The paper investigates properties of the quasi‑Fredholm resolvent set of operators on infinite‑dimensional Banach spaces and examines how the single‑valued extension property (SVEP) behaves under compact perturbations, especially on Hilbert spaces.

Abstract

In this paper we explore some characteristics of the quasi-Fredholm resolvent set $ρ_{qf}(T)$ of an operator $T$ defined on an infinite dimensional Banach space $X$. Moreover, in the case of Hilbert space $H$, we study the stability of the SVEP and describe the operators for which the SVEP is preserved under compact perturbations using quasi-Fredholm spectrum and $ρ_{qf}(T)$.

10 pages

Topics & keywords

#quasi-fredholm spectrum#compact perturbations#sv ep#operator theory#banach spaces#hilbert spacesquasi-fredholm resolvent setSVEPcompact perturbationsHilbert spaceBanach space