Representations of Linear Operators Between Banach Spaces
Representations of Linear Operators Between Banach Spaces

Author: David E. Edmunds

Publisher: Springer Science & Business Media

Published: 2013-09-04

Total Pages: 164

ISBN-13: 3034806426

DOWNLOAD EBOOK

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

The Isometric Theory of Classical Banach Spaces
The Isometric Theory of Classical Banach Spaces

Author: H.E. Lacey

Publisher: Springer

Published: 2011-12-07

Total Pages: 0

ISBN-13: 9783642657641

DOWNLOAD EBOOK

The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1

Sobolev Spaces on Metric Measure Spaces
Sobolev Spaces on Metric Measure Spaces

Author: Juha Heinonen

Publisher: Cambridge University Press

Published: 2015-02-05

Total Pages: 447

ISBN-13: 1316241033

DOWNLOAD EBOOK

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincaré inequalities.

Advanced Functional Analysis
Advanced Functional Analysis

Author: Eberhard Malkowsky

Publisher: CRC Press

Published: 2019-02-25

Total Pages: 446

ISBN-13: 0429809557

DOWNLOAD EBOOK

Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research

Linear Analysis and Representation Theory
Linear Analysis and Representation Theory

Author: Steven A. Gaal

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 701

ISBN-13: 3642807410

DOWNLOAD EBOOK

In an age when more and more items. are made to be quickly disposable or soon become obsolete due to either progress or other man caused reasons it seems almost anachronistic to write a book in the classical sense. A mathematics book becomes an indespensible companion, if it is worthy of such a relation, not by being rapidly read from cover to cover but by frequent browsing, consultation and other occasional use. While trying to create such a work I tried not to be encyclopedic but rather select only those parts of each chosen topic which I could present clearly and accurately in a formulation which is likely to last. The material I chose is all mathematics which is interesting and important both for the mathematician and to a large extent also for the mathematical physicist. I regret that at present I could not give a similar account on direct integrals and the representation theory of certain classes of Lie groups. I carefully kept the level of presentation throughout the whole book as uniform as possible. Certain introductory sections are kept shorter and are perhaps slightly more detailed in order to help the newcomer prog ress with it at the same rate as the more experienced person is going to proceed with his study of the details.

An Introduction to Banach Space Theory
An Introduction to Banach Space Theory

Author: Robert E. Megginson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 613

ISBN-13: 1461206030

DOWNLOAD EBOOK

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Spectral Theory and Analysis
Spectral Theory and Analysis

Author: Jan Janas

Publisher: Springer Science & Business Media

Published: 2011-03-29

Total Pages: 180

ISBN-13: 3764399945

DOWNLOAD EBOOK

This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing important results presented at the conference, some with extended review sections, as well as presentations by young researchers. Special sessions were devoted to random and quasi-periodic differential operators, orthogonal polynomials, Jacobi and CMV matrices, and quantum graphs. This volume also reflects new trends in spectral theory, where much emphasis is given to operators with magnetic fields and non-self-adjoint problems. The book is geared towards scientists from advanced undergraduate students to researchers interested in the recent development on the borderline between operator theory and mathematical physics, especially spectral theory for Schrödinger operators and Jacobi matrices.

Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach
Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach

Author: Miguel Cabrera García

Publisher: Cambridge University Press

Published: 2018-04-12

Total Pages: 759

ISBN-13: 1108570763

DOWNLOAD EBOOK

This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

Foundations of Functional Analysis
Foundations of Functional Analysis

Author: Saminathan Ponnusamy

Publisher: Alpha Science Int'l Ltd.

Published: 2002

Total Pages: 484

ISBN-13: 9781842650790

DOWNLOAD EBOOK

Provides fundamental concepts about the theory, application and various methods involving functional analysis for students, teachers, scientists and engineers. Divided into three parts it covers: Basic facts of linear algebra and real analysis. Normed spaces, contraction mappings, linear operators between normed spaces and fundamental results on these topics. Hilbert spaces and the representation of continuous linear function with applications. In this self-contained book, all the concepts, results and their consequences are motivated and illustrated by numerous examples in each chapter with carefully chosen exercises.

Banach Spaces and their Applications in Analysis
Banach Spaces and their Applications in Analysis

Author: Beata Randrianantoanina

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 465

ISBN-13: 3110918293

DOWNLOAD EBOOK

In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.