Some results on Fredholm and semi-Fredholm perturbations

2016

Abstract. In this paper, we study a detailed treatment of some subsets of M-essential spectra of closed linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators and we investigate some properties of the M-essential spectra of 2 × 2 matrix operator acting on a Banach space. This study led us to generalize some well known results for essential spectra of closed linear operator.

Journal of Mathematical Analysis and Applications, 1998

In this paper, after a characterization of a class of bounded Fredholm operators on Banach spaces, we investigate the essential spectra of closed, densely defined linear operators on L spaces. The obtained results are used to describe the p essential spectra of one-dimensional transport equations with general boundary conditions.

Filomat, 2016

We consider some geometric characteristics of bounded operators on Banach spaces concerning the sets of upper and lower semi-Browder operators and left and right Browder operators. Using various operational quantities we give some perturbation results for upper and lower semi-Fredholm, Weyl and semi-Browder operators as well as for left and right Fredolm, Weyl and Browder operators.

Acta Mathematica Scientia, 2014

In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.

Filomat, 2015

In the present paper, we use the notion of measure of noncompactness to give some results on Fredholm operators and we establish a fine description of the essential approximate point spectrum and the essential defect spectrum of a closed densely defined linear operator.

Advances in Pure Mathematics

This paper consists of some properties of a new subclass of semigroup of linear operator. The stability and spectra analysis of ω-order preserving partial contraction mapping (ω-OCP n) are obtained. The results show that operators on the proposed ω-OCP n are densely defined and closed. Several existing results in the literature are contained in this work.

Acta Mathematica Sinica, English Series, 2010

Multivalued semi-Fredholm type linear operators with complemented ranges and null spaces are introduced. Conditions are obtained under which the classes given are stable under compact, strictly singular and strictly cosingular additive perturbations. We adher to the notation and terminology of the book [3]: X and Y are normed spaces, B X the closed unit ball of X, X the dual space of X and P(X) denotes the class of all closed finite-codimensional subspaces of X. If M is a subspace of X, then M ⊥ := {x ∈ X : x (x) = 0, x ∈ M }.

We extend the technique used by Kordula and Muller to show that the stability radius of a quasi-Fredholm operator T is the limit of (Tn)1=n as n !1 . If 0 is an isolated point of the Apostol spectrum (T ), then the above limit is non-zero if and only if T is quasi-Fredholm. Let L(X) be the set of all bounded linear operators on a complex Banach space X. For any T 2 L(X), we denote the null space and range of T by N (T )a nd R ( T ) respectively. The Apostol spectrum of T is dened to be the set (T )= f 2 C: lim ! (T I )=0 g ; (1)

Mathematica Bohemica

We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener's sense coincide. Additional illustrative results are given too.

2019

A Banach space operator T obeys property (gm) if the<br> isolated points of the spectrum σ(T) of T which are eigenvalues<br> are exactly those points λ of the spectrum for which T − λI is<br> a left Drazin invertible. In this article, we study the stability of<br> property (gm), for a bounded operator acting on a Banach space,<br> under perturbation by finite rank operators, by nilpotent operators,<br> by quasi-nilpotent operators, or more generally by algebraic operators<br> commuting with T.

Afrika Matematika, 2018

In this paper, we study the stability of some essential B-spectra of closed linear operators on a Banach space X , under polynomially finite rank operators and we give the characterization of some essential B-spectra of a 2 × 2 of unbounded matrix operator acting in the product of Banach spaces X × Y. Then, using the functional calculus, we prove that a spectral mapping type theorem holds for these essential B-spectra. As an application, we study the effect of the functional calculus on the class of meromorphic operators, and on the class of isoloid operators with sable sign index, satisfying generalized Weyl theorem.

Archiv der Mathematik, 2001

Linear operators in Banach and Hilbert spaces are considered. Bounds for the spectrum are established under relatively bounded perturbations. An application to nonselfadjoint differential operators is discussed.

arXiv: Functional Analysis, 2020

Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X, where F is a C^1-operator, and C a C^1 compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a C^1-diffeomorphism. Three corollaries are given. The first one, when F is a linear homeomorphism. The second one, when F is a k-contractive perturbation of the identity. The third one, when X is a Hilbert space and F a particular linear operator. The proof of our results is based on properties of Fredholm operators, as well as on local and global inverse mapping theorems, and the Banach fixed point theorem. As an application two examples are given

Mathematica Bohemica, 2020

We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded $p$-variation in Wiener's sense coincide. Additional illustrative results are given too

Turk J Math, 2009

Let T, A be operators with domains D (T)⊆ D (A) in a normed space X. The operator A is called T-bounded if Ax≤ ax+bTx for some a, b≥ 0 and all x∈ D (T). If A has the Hyers–Ulam stability then under some suitable assumptions we show that both T and S:= A+T ...