Characterization of Relatively Demicompact Operators by Means of Measures of Noncompactness (original) (raw)

Some Fredholm Theory Results Around Relative Demicompactness Concept

2021

In this paper, we provide a characterization of upper semiFredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

Applications of measure of noncompactness in operators on the spaces sα,sα0,sα(c),ℓαp

Journal of Mathematical Analysis and Applications, 2006

In this paper, we characterize some operators and matrix transformations in the sequence spaces s α , s 0 α , s (c) α , p α. Moreover, using the Hausdorff measure of noncompactness necessary and sufficient conditions are formulated for a linear operator between the mentioned spaces to be compact. Among other things, some results of Cohen and Dunford are recovered.

Some results in Fredholm theory via the measure of noncompactness

Applied Mathematical Sciences, 2015

Let A be a bounded linear operator in a complex Banach space X. We show that Id X − A is a Fredholm operator provided that A has a sufficiently small polynomially measure of noncompactness. In our general framework, we note that the case of Riesz operator becomes a particular one as it is for the other results in the domain. This enable us to obtain a new characterization for the Weyl essential spectrum of a closed densely defined operators.

Semicompact operators

Indagationes Mathematicae, 1990

In the following let E and F be arbitrary Banach lattices and assume that Fis Dedekind complete.

Spectral properties for generalized weakly S-demicompact operators

Linear and Multilinear Algebra, 2020

In this paper, we introduce the concept of generalized weakly S-demicompact operators with respect to a weakly closed linear operator S. We study the general setting of Fredholm theory. We give some perturbation results on the behaviour of relative essential spectra of the sum of two bounded linear operators by means of the relative essential spectra of each one. A characterization of generalized weakly S-demicompact operators by means of measures of weak noncompactness is given. Moreover, we impose some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak S-demicompactness of its closure.

Spectral Properties Involving Generalized Weakly Demicompact Operators

Mediterranean Journal of Mathematics

In this article, we introduce the notion of polynomial demicompactness and we use it to give some results on Fredholm operators and to establish a fine description of some essential spectra of a closed densely defined linear operator. Our work is a generalization of many known ones in the literature.

Measure of noncompactness for compact matrix operators on some BK spaces

Filomat, 2014

In this paper, we characterize the matrix classes (?1, ??p )(1? p < 1). We also obtain estimates for the norms of the bounded linear operators LA defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

Generalized measures of noncompactness of sets and operators in Banach spaces

Acta Mathematica Hungarica, 2010

New measures of noncompactness for bounded sets and linear operators, in the setting of abstract measures and generalized limits, are constructed. A quantitative version of a classical criterion for compactness of bounded sets in Banach spaces by R. S. Phillips is provided. Properties of those measures are established and it is shown that they are equivalent to the classical measures of noncompactness. Applications to summable families of Banach spaces, interpolations of operators and some consequences are also given.

The Hausdorff measure of noncompactness of matrix operators on some BK spaces

Operators and Matrices, 2011

In the present paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces c λ 0 and λ ∞ which have recently been introduced in [On the spaces of λ -convergent and bounded sequences, Thai J. Math. 8(2) (2010) 311-329]. Further, by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces. Mathematics subject classification (2010): 46B15, 46B45, 46B50.