1,720,993 research outputs found
A characterization of the Schechter essential spectrum on Banach spaces and applications
No full textAbstractIn a recent article by the author (C. R. Acad. Sci. Paris Sér. I 331 (2000) 525–530; Boll. Un. Mat. Ital. (2002), to appear) the Schechter spectrum of closed, densely defined linear operators has been characterized on spaces, which possess the Dunford–Pettis property or which are isomorphic to one of the spaces Lp(Ω), p>1. The purpose of the present work is to extend this analysis to the case of Banach spaces. Further we apply the obtained results to investigate the Schechter essential spectrum of one-dimensional transport equations with different boundary conditions
Spectral theory and applications of linear operators and block operator matrices
No full textExamining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially compact operators
Some remarks on the Schechter essential spectrum and applications to transport equations
No full textAbstractThe purpose of this article is to provide an extension of the work [A. Jeribi, J. Math. Anal. Appl. 271 (2002) 343–358] where a detailed treatment of the Schechter essential spectrum of a closed densely defined linear operators A subjected to additive perturbations K such that (λ−A)−1K or K(λ−A)−1 belonging to arbitrary subsets of L(X) (where X denotes a Banach spaces) contained in the ideal of Fredholm perturbations. Our approach consists principally in considering the class of A-closable (not necessarily bounded) which contained in the set of A-resolvent Fredholm perturbations (see Definition 1.12). They are used to describe the Schechter essential spectrum of singular neutron transport equations in bounded geometries
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Symmetric family of Fredholm operators of indices zero, stability of essential spectra and application to transport operators
No full textAbstractIn this paper, we prove that, if the product A=A1⋯An is a Fredholm operator where the ascent and descent of A are finite, then Aj is a Fredholm operator of index zero for all j, 1⩽j⩽n, where A1,…,An be a symmetric family of bounded operators. Next, we investigate a useful stability result for the Rakočević/Schmoeger essential spectra. Moreover, we show that some components of the Fredholm domains of bounded linear operators on a Banach space remain invariant under additive perturbations belonging to broad classes of operators A such as γ(Am)<1 where γ(⋅) is a measure of noncompactness. We also discuss the impact of these results on the behavior of the Rakočević/Schmoeger essential spectra. Further, we apply these latter results to investigate the Rakočević/Schmoeger essential spectra for singular neutron transport equations in bounded geometries
Nonlinear functional analysis in Banach spaces and Banach algebras: fixed point theory under weak topology for nonlinear operators and block operator matrices with applications
No full textUncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exte
A characterization of some subsets of Schechter's essential spectrum and application to singular transport equation
No full textAbstractThe purpose of this paper is to provide a detailed treatment of some subsets of Schechter's essential spectrum of closed, densely defined linear operators subjected to additive perturbations. Our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries
Holomorphically Weyl-decomposably regular
No full textInternational audienceWe consider left and right Fredholm-decomposably regular operators introduced in [23], and the corresponding holomorphic versions. Using their results established by Zeng in [23], we give new properties of these classes of operators. We introduce the concept of Weyl-decomposably regular operator and the corresponding holomorphic version in the setting of L(X), where L(X) is the set of all bounded operators from Banach space X to X, and we give various characterizations of this class of operators
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