Fredholm And Local Spectral Theory Ii PDF Download
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Author | : Pietro Aiena |
Publisher | : Springer |
Total Pages | : 546 |
Release | : 2018-11-24 |
Genre | : Mathematics |
ISBN | : 3030022668 |
Download Fredholm and Local Spectral Theory II Book in PDF, ePub and Kindle
This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.
Author | : Pietro Aiena |
Publisher | : Springer Science & Business Media |
Total Pages | : 452 |
Release | : 2007-05-08 |
Genre | : Mathematics |
ISBN | : 1402025254 |
Download Fredholm and Local Spectral Theory, with Applications to Multipliers Book in PDF, ePub and Kindle
A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
Author | : K. B. Laursen |
Publisher | : Oxford University Press |
Total Pages | : 610 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780198523819 |
Download An Introduction to Local Spectral Theory Book in PDF, ePub and Kindle
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Author | : Pietro Aiena |
Publisher | : |
Total Pages | : |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Fredholm and Local Spectral Theory Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1994 |
Genre | : |
ISBN | : |
Download Multipliers and Local Spectral Theory Book in PDF, ePub and Kindle
Author | : Jürgen Appell |
Publisher | : Walter de Gruyter |
Total Pages | : 420 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 3110181436 |
Download Nonlinear Spectral Theory Book in PDF, ePub and Kindle
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Author | : Anna Maria Candela |
Publisher | : Springer Nature |
Total Pages | : 470 |
Release | : 2023-06-21 |
Genre | : Mathematics |
ISBN | : 3031200217 |
Download Recent Advances in Mathematical Analysis Book in PDF, ePub and Kindle
This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.
Author | : Dragana S. Cvetković Ilić |
Publisher | : American Mathematical Society |
Total Pages | : 170 |
Release | : 2022-06-07 |
Genre | : Mathematics |
ISBN | : 1470469871 |
Download Completion Problems on Operator Matrices Book in PDF, ePub and Kindle
Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.
Author | : Carlos S. Kubrusly |
Publisher | : Springer Nature |
Total Pages | : 249 |
Release | : 2020-01-30 |
Genre | : Mathematics |
ISBN | : 3030331490 |
Download Spectral Theory of Bounded Linear Operators Book in PDF, ePub and Kindle
This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.
Author | : Luigi Rodino |
Publisher | : Springer Science & Business Media |
Total Pages | : 456 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780792345442 |
Download Microlocal Analysis and Spectral Theory Book in PDF, ePub and Kindle
There has been considerable progress in the field of microlocal analysis. In a broad sense the subject is the modern version of the classical Fourier technique for solving partial differential equations, with the localization process taking account of dual variables. The tools of pseudo-differential operators, wave-front sets and Fourier integral operators have now conferred a mature form on the theory of linear partial differential operators in the frame of Schwartz distributions or other generalized functions. At the same time, microlocal analysis has assumed an important role as an independent part of analysis, with other applications throughout mathematics and physics, one major theme being spectral theory for the Schrodinger equation in quantum mechanics.