Author: Izrailʹ Moiseevich GelʹfandPublisher:
ISBN:
Category : Banach algebras
Languages : en
Pages : 306
Book Description
Commutative Normed Rings, By I. Gelfand, D. Raikov, and G. Shilov
Author: Izrailʹ Moiseevich GelʹfandPublisher:
ISBN:
Category : Banach algebras
Languages : en
Pages : 306
Book Description
Commutative Normed Rings
Author: I. GelfandPublisher: American Mathematical Society
ISBN: 0821829726
Category : Mathematics
Languages : en
Pages : 308
Book Description
From the Preface (1960): “This book is devoted to an account of one of the branches of functional analysis, the theory of commutative normed rings, and the principal applications of that theory. It is based on [the authors'] paper written … in 1940, hard on the heels of the initial period of the development of this theory … The book consists of three parts. Part one, concerned with the theory of commutative normed rings and divided into two chapters; the first containing foundations of the theory and the second dealing with more special problems. Part two deals with applications to harmonic analysis and is divided into three chapters. The first chapter discusses the ring of absolutely integrable functions on a line with convolution as multiplication and finds the maximal ideals of this ring and some of its analogues. In the next chapter, these results are carried over to arbitrary commutative locally compact groups and they are made the foundation of the construction of harmonic analysis and the theory of characters. A new feature here is the construction of an invariant measure on the group of characters and a proof of the inversion formula for Fourier transforms that is not based on theorems on the representation of positive-definite functions or positive functionals … The last chapter of the second part—the most specialized of all the chapters—is devoted to the investigation of the ring of functions of bounded variation on a line with multiplication defined as convolution, including the complete description of the maximal ideals of this ring. The third part of the book is devoted to the discussion of two important classes of rings of functions: regular rings and rings with uniform convergence. The first of the chapters essentially studies the structure of ideals in regular rings. The chapter ends with an example of a ring of functions having closed ideals that cannot be represented as the intersections of maximal ideals. The second chapter discusses the ring $C(S)$ of all bounded continuous complex functions on completely regular spaces $S$ and various of its subrings … Since noncommutative normed rings with an involution are important for group-theoretical applications, the paper by I. M. Gelfand and N. A. Naimark, ‘Normed Rings with an Involution and their Representations’, is reproduced at the end of the book, slightly abridged, in the form of an appendix … This monograph also contains an account of the foundations of the theory of commutative normed rings without, however, touching upon the majority of its analytic applications … The reader [should] have knowledge of the elements of the theory of normed spaces and of set-theoretical topology. For an understanding of the fourth chapter, [the reader should] also know what a topological group is. It stands to reason that the basic concepts of the theory of measure and of the Lebesgue integral are also assumed to be known …”
Commutative Normed Rings
Author: I. M. Gel'fandPublisher:
ISBN:
Category : Banach algebras
Languages : en
Pages : 306
Book Description
Commutative Normed Rings
Author: Izrailʹ Moiseevich GelʹfandPublisher: Chelsea Publishing Company, Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 328
Book Description
Commutative Normed Rings
Author: I.M. GelfandFundamentals of Infinite Dimensional Representation Theory
Author: Raymond C. FabecPublisher: CRC Press
ISBN: 1482285770
Category : Mathematics
Languages : en
Pages : 448
Book Description
Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.
Modular Representation Theory and Commutative Banach Algebras
Author: David J. BensonPublisher: American Mathematical Society
ISBN: 1470470292
Category : Mathematics
Languages : en
Pages : 130
Book Description
View the abstract.
Concrete Functional Calculus
Author: R. M. DudleyPublisher: Springer Science & Business Media
ISBN: 1441969500
Category : Mathematics
Languages : en
Pages : 675
Book Description
Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.
Function Spaces
Author: Krzysztof JaroszPublisher: American Mathematical Soc.
ISBN: 0821809393
Category : Mathematics
Languages : en
Pages : 384
Book Description
This proceedings volume presents 36 papers given by leading experts during the Third Conference on Function Spaces held at Southern Illinois University at Edwardsville. A wide range of topics in the subject area are covered. Most papers are written for nonexperts, so the book can serve as a good introduction to the topic for those interested in this area. The book presents the following broad range of topics, including spaces and algebras of analytic functions of one and of many variables, $Lp$ spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces and related subjects. Known results, open problems, and new discoveries are featured. At the time of publication, information about the book, the conference, and a list and pictures of contributors are available on the Web at www.siue.edu/MATH/conference.htm.
Principal Structures and Methods of Representation Theory
Author: Dmitriĭ Petrovich ZhelobenkoPublisher: American Mathematical Soc.
ISBN: 9780821889671
Category : Mathematics
Languages : en
Pages : 456
Book Description
The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups,along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Liealgebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.