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Author : Ernest A. Michael
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 43,8 Mb
Release : 1952
Category : Banach algebras
ISBN : 9780821812112
Author : Ernest Alexander Michael
Publisher : Unknown
Page : 82 pages
File Size : 43,9 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:256405543
Author : A Lau,I Tweddle
Publisher : CRC Press
Page : 284 pages
File Size : 52,5 Mb
Release : 1995-05-15
Category : Mathematics
ISBN : 0582257778
This volume contains the proceedings of an international conference held to mark the retirement of Professor Taqdir Husain from McMaster University. The contributions, covering topics such as topological vector spaces, topological algebras and related areas, reflect Husain's research interests and present surveys and new research in the topics of the conference.
Author : Anastasios Mallios,Marina Haralampidou
Publisher : American Mathematical Soc.
Page : 442 pages
File Size : 53,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838686
The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the ""non-normed"" case. In addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and $K$-theory.
Author : Maria Fragoulopoulou,Camillo Trapani
Publisher : Springer Nature
Page : 267 pages
File Size : 44,5 Mb
Release : 2020-04-07
Category : Mathematics
ISBN : 9783030377052
This book offers a review of the theory of locally convex quasi *-algebras, authored by two of its contributors over the last 25 years. Quasi *-algebras are partial algebraic structures that are motivated by certain applications in Mathematical Physics. They arise in a natural way by completing a *-algebra under a locally convex *-algebra topology, with respect to which the multiplication is separately continuous. Among other things, the book presents an unbounded representation theory of quasi *-algebras, together with an analysis of normed quasi *-algebras, their spectral theory and a study of the structure of locally convex quasi *-algebras. Special attention is given to the case where the locally convex quasi *-algebra is obtained by completing a C*-algebra under a locally convex *-algebra topology, coarser than the C*-topology. Introducing the subject to graduate students and researchers wishing to build on their knowledge of the usual theory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.
Author : A. Mallios
Publisher : Elsevier
Page : 534 pages
File Size : 42,7 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872352
This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far one can go beyond the classical framework of Banach algebras while still retaining substantial results. The need for such an extension of the standard theory of normed algebras has been apparent since the early days of the theory of topological algebras, most notably the locally convex ones. It is worth noticing that the previous demand was due not only to theoretical reasons, but also to potential concrete applications of the new discipline.
Author : M. Fragoulopoulou
Publisher : Elsevier
Page : 514 pages
File Size : 43,9 Mb
Release : 2005-07-26
Category : Mathematics
ISBN : 9780080461229
This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common. Key features: - Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers. - Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.
Author : Alexander Katz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 317 pages
File Size : 47,6 Mb
Release : 2018-05-07
Category : Mathematics
ISBN : 9783110414424
Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems
Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 820 pages
File Size : 54,5 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 : Joachim Cuntz,Jonathan Rosenberg
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 44,7 Mb
Release : 2007-07-19
Category : Mathematics
ISBN : 9783764383985
Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
Author : Ralf Meyer
Publisher : European Mathematical Society
Page : 376 pages
File Size : 52,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190396
Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to $K$-theory, and the Chern-Connes character for $K$-theory and $K$-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications.
Author : Shozo Koshi
Publisher : World Scientific
Page : 282 pages
File Size : 55,8 Mb
Release : 1991-10-31
Category : Electronic
ISBN : 9789814555920
The objective of this symposium is to discuss the recent developments in the various areas of functional analysis. This volume consists mainly of articles in the fields of topological algebra, Banach spaces, function spaces, harmonic analysis, operator theory and application of functional analysis.
Author : A.Y. Helemskii
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 47,7 Mb
Release : 1989-10-31
Category : Mathematics
ISBN : 0792302176
'Et moi *.... si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aUe.' it belongs. on the topmost shelf next Jules Verne where to the dusty canister labelled 'discarded non· The series is divergent: therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Hugo Arizmendi,Carlos Bosch,Lourdes Palacios
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 54,9 Mb
Release : 2004
Category : Topological algebras
ISBN : 9780821835562
Papers from a July 2002 conference report on recent work in topological algebras, locally convex and Banach spaces, spectral theory, and operator theory. Some specific topics include Gelfand representation of topological algebras, matrix representations of Ambrose algebras, docile locally convex spa
Author : Anonim
Publisher : Elsevier
Page : 369 pages
File Size : 46,9 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 0080871356
This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
