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Normed Algebras

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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 602/5 ( reviews)

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Book Synopsis Normed Algebras by : M.A. Naimark

Download or read book Normed Algebras written by M.A. Naimark. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: book and to the publisher NOORDHOFF who made possible the appearance of the second edition and enabled the author to introduce the above-mentioned modifi cations and additions. Moscow M. A. NAIMARK August 1963 FOREWORD TO THE SECOND SOVIET EDITION In this second edition the initial text has been worked over again and improved, certain portions have been completely rewritten; in particular, Chapter VIII has been rewritten in a more accessible form. The changes and extensions made by the author in the Japanese, German, first and second (= first revised) American, and also in the Romanian (lithographed) editions, were hereby taken into account. Appendices II and III, which are necessary for understanding Chapter VIII, have been included for the convenience of the reader. The book discusses many new theoretical results which have been developing in tensively during the decade after the publication of the first edition. Of course, lim itations on the volume of the book obliged the author to make a tough selection and in many cases to limit himself to simply a formulation of the new results or to pointing out the literature. The author was also compelled to make a choice of the exceptionally extensive collection of new works in extending the literature list. Monographs and survey articles on special topics of the theory which have been published during the past decade have been included in this list and in the litera ture pointed out in the individual chapters.

Complete Normed Algebras

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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 692/5 ( reviews)

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Book Synopsis Complete Normed Algebras by : Frank F. Bonsall

Download or read book Complete Normed Algebras written by Frank F. Bonsall. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.

Non-Associative Normed Algebras

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Release : 2014-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 069/5 ( reviews)

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Book Synopsis Non-Associative Normed Algebras by : Miguel Cabrera García

Download or read book Non-Associative Normed Algebras written by Miguel Cabrera García. This book was released on 2014-07-31. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.

Normed Algebras

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Release : 1979-11-19
Genre :
Kind : eBook
Book Rating : 610/5 ( reviews)

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Book Synopsis Normed Algebras by : M. A. Naimark

Download or read book Normed Algebras written by M. A. Naimark. This book was released on 1979-11-19. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach

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Release : 2018-04-12
Genre : Mathematics
Kind : eBook
Book Rating : 436/5 ( reviews)

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Book Synopsis Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach by : Miguel Cabrera García

Download or read book Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach written by Miguel Cabrera García. This book was released on 2018-04-12. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

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