Introduction To Operator Theory Elements Of Functional Analysis
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Introduction To Operator Theory I
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Author : A. Brown
language : en
Publisher: Springer
Release Date : 2013-06-02
Introduction To Operator Theory I written by A. Brown and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-02 with Mathematics categories.
This book was written expressly to serve as a textbook for a one- or two-semester introductory graduate course in functional analysis. Its (soon to be published) companion volume, Operators on Hilbert Space, is in tended to be used as a textbook for a subsequent course in operator theory. In writing these books we have naturally been concerned with the level of preparation of the potential reader, and, roughly speaking, we suppose him to be familiar with the approximate equivalent of a one-semester course in each of the following areas: linear algebra, general topology, complex analysis, and measure theory. Experience has taught us, however, that such a sequence of courses inevitably fails to treat certain topics that are important in the study of functional analysis and operator theory. For example, tensor products are frequently not discussed in a first course in linear algebra. Likewise for the topics of convergence of nets and the Baire category theorem in a course in topology, and the connections between measure and topology in a course in measure theory. For this reason we have chosen to devote the first ten chapters of this volume (entitled Part I) to topics of a preliminary nature. In other words, Part I summarizes in considerable detail what a student should (and eventually must) know in order to study functional analysis and operator theory successfully.
Introduction To Operator Theory Elements Of Functional Analysis
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Author : Arlen Brown
language : en
Publisher:
Release Date : 1977
Introduction To Operator Theory Elements Of Functional Analysis written by Arlen Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Operator theory categories.
Introduction To Operator Theory Elements Of Functional Analysis
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Author : Arlen Brown
language : en
Publisher:
Release Date : 1977
Introduction To Operator Theory Elements Of Functional Analysis written by Arlen Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Functional analysis categories.
Elements Of Operator Theory
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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Elements Of Operator Theory written by Carlos S. Kubrusly and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
{\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.
Convex Functional Analysis
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Author : Andrew J. Kurdila
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Convex Functional Analysis written by Andrew J. Kurdila and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Science categories.
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Commutative Algebra written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.
Topics In Banach Space Theory
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Author : Fernando Albiac
language : en
Publisher: Taylor & Francis
Release Date : 2006-01-04
Topics In Banach Space Theory written by Fernando Albiac and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-04 with Mathematics categories.
This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.
Algebra
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Author : William A. Adkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebra written by William A. Adkins and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
Elementary Methods In Number Theory
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-11
Elementary Methods In Number Theory written by Melvyn B. Nathanson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Mathematics categories.
This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.
The Geometry Of Syzygies
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-01
The Geometry Of Syzygies written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-01 with Mathematics categories.
First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.