Title
Commutative Normed Rings (English And Russian Edition),New
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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 positivedefinite functions or positive functionals ... The last chapter of the second partthe most specialized of all the chaptersis 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 grouptheoretical 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 settheoretical 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 ... '
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We provide a 2-year limited warranty, from the date of purchase for all our products.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Commutative Normed Rings'? A: The book focuses on the theory of commutative normed rings, a branch of functional analysis, and its principal applications, exploring foundational concepts and specialized problems.
- Q: Who is the author of this book? A: The author of 'Commutative Normed Rings' is I. Gelfand.
- Q: What is the publication date of this book? A: The book was published on October 4, 1999.
- Q: What is the condition of the book? A: This is a used book in good condition.
- Q: How many pages does 'Commutative Normed Rings' have? A: The book contains 306 pages.
- Q: What type of binding does this book have? A: The book is bound in hardcover.
- Q: What prior knowledge is recommended for readers of this book? A: Readers should have knowledge of normed spaces, set-theoretical topology, and the basics of measure theory and the Lebesgue integral.
- Q: Does the book include any appendices or supplementary materials? A: Yes, the book includes an appendix reproducing a paper on noncommutative normed rings with an involution by I. M. Gelfand and N. A. Naimark.
- Q: What are the main parts of the book? A: The book is divided into three parts: the theory of commutative normed rings, applications to harmonic analysis, and discussions on regular rings and uniform convergence.
- Q: Is this book suitable for beginners in functional analysis? A: The book assumes a certain level of prior knowledge in functional analysis, making it more suitable for readers with some background in the subject.