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Author : Charles Earl Rickart
Publisher : Krieger Publishing Company
Page : 416 pages
File Size : 55,6 Mb
Release : 1974
Category : Algebraic fields
ISBN : UOM:39076005234385
Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 820 pages
File Size : 40,7 Mb
Release : 1994-03-25
Category : Mathematics
ISBN : 0521366372
This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 846 pages
File Size : 52,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0521366380
This second of two volumes gives a modern exposition of the theory of Banach algebras.
Author : Anonim
Publisher : Elsevier
Page : 440 pages
File Size : 43,6 Mb
Release : 2001-07-11
Category : Mathematics
ISBN : 9780080528342
General Theory of C*-Algebras
Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 834 pages
File Size : 55,9 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521366380
This second volume of a two-volume set provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. The author emphasizes the roles of *-algebra structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. Proofs are presented in complete detail at a level accessible to graduate students. The books contain a wealth of historical comments, background material, examples, and an extensive bibliography. Together they constitute the standard reference for the general theory of *-algebras. This second volume deals with *-algebras. Noteworthy chapters develop the theory of *-algebras without additional restrictions, going well beyond what has been proved previously in this context and describe locally compact groups and the *-algebras related to them.
Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 812 pages
File Size : 47,8 Mb
Release : 1994-03-25
Category : Mathematics
ISBN : 0521366372
This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Author : Eberhard Kaniuth
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 50,5 Mb
Release : 2008-12-16
Category : Mathematics
ISBN : 9780387724768
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.
Author : H. Garth Dales
Publisher : Cambridge University Press
Page : 338 pages
File Size : 41,5 Mb
Release : 2003-11-13
Category : Mathematics
ISBN : 0521535840
Table of contents
Author : Peter Harmand,Dirk Werner,Wend Werner
Publisher : Springer
Page : 390 pages
File Size : 45,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477532
This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.
Author : Theodore W. Palmer
Publisher : Unknown
Page : 357 pages
File Size : 47,6 Mb
Release : 2001
Category : Banach algebras
ISBN : 0521183324
Author : Anonim
Publisher : Unknown
Page : 264 pages
File Size : 40,9 Mb
Release : 1982
Category : Securities
ISBN : MINN:30000007281862
Author : Harold G. Dales
Publisher : Oxford University Press on Demand
Page : 907 pages
File Size : 46,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0198500130
Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras, and shows how their topology is often determined by their algebraic structure: the central questions ask when homomorphisms and derivations from Banach algebras are automatically continuous, and seek canonical forms for these maps. The book synthesizes work over the last 20 years, and givesa definitive account; there are many new and unpublished results. The book describes many specific classes of Banach algebras, including function algebras, group algebras, algebras of operators, C*-algebras, and radical Banach algebras; it is a compendium of results on these examples. The subject interweaves algebra, functional analysis, and complex analysis, and has a dash of set theory and logic; the background in all these areas is fully explained. This volume is essential reading for anyone interested in any aspect of this vast subject.
Author : Yurii I. Lyubich
Publisher : Birkhäuser
Page : 231 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891691
The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.
Author : Gerald J. Murphy
Publisher : Academic Press
Page : 297 pages
File Size : 44,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080924960
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Author : Steffen Roch,Pedro A. Santos,Bernd Silbermann
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 42,9 Mb
Release : 2010-11-19
Category : Mathematics
ISBN : 9780857291837
Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.