Author: John D. WilkesPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Structure of Commutative Normed Rings
Author: John D. WilkesCommutative 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: Izrailʹ Moiseevich GelʹfandPublisher: Chelsea Publishing Company, Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 328
Book Description
Commutative Normed Rings
Author: I. M. Gel'fandPublisher:
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.M. GelfandStructure of Rings
Author: Nathan JacobsonPublisher: American Mathematical Soc.
ISBN: 0821810375
Category : Mathematics
Languages : en
Pages : 311
Book Description
The main purpose of this volume is to give an account of the important developments in the theory of (non-commutative) rings. These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of non-semi-simple rings (Frobenius algebras, quasi-Frobenius rings).
Commutative Normed Rings. Gelfand
Author: Izrail Moiseevich GelfandPublisher:
ISBN:
Category :
Languages : en
Pages : 306
Book Description
Noncommutative Rings
Author: I. N. HersteinPublisher: American Mathematical Soc.
ISBN: 088385015X
Category : Mathematics
Languages : en
Pages : 202
Book Description
Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.
An Introduction to the Mathematical Structure of Quantum Mechanics
Author: F. StrocchiPublisher: World Scientific
ISBN: 9812835229
Category : Science
Languages : en
Pages : 193
Book Description
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.