Topological Algebras And Applications

Author : Anastasios Mallios,Marina Haralampidou
Publisher : American Mathematical Soc.
Page : 442 pages
File Size : 44,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838686

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Topological Algebras and Applications by Anastasios Mallios,Marina Haralampidou Pdf

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 : V.K. Balachandran
Publisher : Elsevier
Page : 460 pages
File Size : 52,6 Mb
Release : 2000-11-23
Category : Mathematics
ISBN : 0080543081

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Topological Algebras by V.K. Balachandran Pdf

This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-matter of Chapter 7. Chapter 8 deals with commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.

Author : Alexander Katz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 317 pages
File Size : 45,6 Mb
Release : 2018-05-07
Category : Mathematics
ISBN : 9783110413557

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Topological Algebras and their Applications by Alexander Katz Pdf

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 : Hugo Arizmendi,Carlos Bosch,Lourdes Palacios
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 40,5 Mb
Release : 2004
Category : Topological algebras
ISBN : 9780821835562

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Topological Algebras and Their Applications by Hugo Arizmendi,Carlos Bosch,Lourdes Palacios Pdf

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 : A. Mallios
Publisher : Elsevier
Page : 534 pages
File Size : 50,5 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872352

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Topological Algebras by A. Mallios Pdf

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 : David E. Evans,Masamichi Takesaki
Publisher : Cambridge University Press
Page : 257 pages
File Size : 40,5 Mb
Release : 1988
Category : Mathematics
ISBN : 9780521368438

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Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology by David E. Evans,Masamichi Takesaki Pdf

These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

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

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The Homology of Banach and Topological Algebras by A.Y. Helemskii Pdf

'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 : Alain Guichardet
Publisher : Unknown
Page : 228 pages
File Size : 40,6 Mb
Release : 1968
Category : Mathematics
ISBN : UCAL:B3773741

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Special Topics in Topological Algebras by Alain Guichardet Pdf

Based on seminars on commutative Banach algebras, Von Neumann algebras, topological algebras and holomorphic functions.

Author : Mahima Ranjan Adhikari
Publisher : Springer
Page : 615 pages
File Size : 50,6 Mb
Release : 2016-09-16
Category : Mathematics
ISBN : 9788132228431

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Basic Algebraic Topology and its Applications by Mahima Ranjan Adhikari Pdf

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Author : Alexander Arhangel’skii,Mikhail Tkachenko
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 43,5 Mb
Release : 2008-05-01
Category : Mathematics
ISBN : 9789491216350

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Topological Groups and Related Structures, An Introduction to Topological Algebra. by Alexander Arhangel’skii,Mikhail Tkachenko Pdf

Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.

Author : Carlos Bosch,Hugo Arizmendi,Lourdes Palacios
Publisher : Unknown
Page : 137 pages
File Size : 47,8 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:474499398

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Topological Algebras and Their Applications by Carlos Bosch,Hugo Arizmendi,Lourdes Palacios Pdf

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 : F. Borceux,G. Van den Bossche
Publisher : Springer
Page : 249 pages
File Size : 46,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386964

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Algebra in a Localic Topos with Applications to Ring Theory by F. Borceux,G. Van den Bossche Pdf

Author : A.Y. Helemskii
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400923546

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The Homology of Banach and Topological Algebras by A.Y. Helemskii Pdf

'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 : Hal Schenck
Publisher : Springer Nature
Page : 231 pages
File Size : 52,6 Mb
Release : 2022-11-21
Category : Mathematics
ISBN : 9783031066641

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Algebraic Foundations for Applied Topology and Data Analysis by Hal Schenck Pdf

This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user’s guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.

Author : Alexander Katz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 317 pages
File Size : 50,8 Mb
Release : 2018-05-07
Category : Mathematics
ISBN : 9783110414424

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Topological Algebras and their Applications by Alexander Katz Pdf

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