Banach Space Theory

The Basis for Linear and Nonlinear Analysis

Author: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

Publisher: Springer Science & Business Media

ISBN: 9781441975157

Category: Mathematics

Page: 820

View: 3708

DOWNLOAD NOW »

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Release

FUNCTIONAL ANALYSIS

A FIRST COURSE

Author: M. THAMBAN NAIR

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120317351

Category: Mathematics

Page: 448

View: 9725

DOWNLOAD NOW »

Intended as an introductory-level text on Functional Analysis for the postgraduate students in Mathematics, this compact and well-organized text covers all the topics considered essential to the subject. In so doing, it provides a very good understanding of the subject to the reader. The book begins with a review of linear algebra, and then it goes on to give the basic notion of a norm on linear space (proving thereby most of the basic results), progresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis. Besides, the book analyzes more advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators. The text is so organized that it strives, particularly in the last chapter, to apply and relate the basic theorems to problems which arise while solving operator equations.
Release

A Second Course in Linear Algebra

Author: Stephan Ramon Garcia,Roger A. Horn

Publisher: Cambridge University Press

ISBN: 1107103819

Category: Mathematics

Page: 426

View: 6019

DOWNLOAD NOW »

A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.
Release

Measures, Integrals and Martingales

Author: René L. Schilling

Publisher: Cambridge University Press

ISBN: 9780521850155

Category: Mathematics

Page: 381

View: 8110

DOWNLOAD NOW »

This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.
Release

Functional Analysis

An Introduction

Author: Yuli Eidelman,Vitali D. Milman,Antonis Tsolomitis

Publisher: American Mathematical Soc.

ISBN: 0821836463

Category: Mathematics

Page: 322

View: 567

DOWNLOAD NOW »

The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively), and it is as self-contained as possible. The only prerequisites for the first part are minimal amounts of linear algebra and calculus. However, for the second course (Part II), it is useful to have some knowledge of topology and measure theory. Each chapter is followed by numerous exercises, whose solutions are given at the end of the book.
Release

Matrix Theory

Basic Results and Techniques

Author: Fuzhen Zhang

Publisher: Springer Science & Business Media

ISBN: 1461410991

Category: Mathematics

Page: 399

View: 2998

DOWNLOAD NOW »

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.
Release

A Course in Mathematical Analysis

Author: D. J. H. Garling

Publisher: Cambridge University Press

ISBN: 1107032032

Category: Mathematics

Page: 336

View: 3417

DOWNLOAD NOW »

The second volume of three providing a full and detailed account of undergraduate mathematical analysis.
Release