Lectures On Amenability

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Lectures on Amenability

Volker Runde
Lectures on Amenability Book PDF

Author : Volker Runde
Publisher : Springer
Page : 302 pages
File Size : 50,6 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540455608

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Lectures on Amenability by Volker Runde Pdf

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Amenable Banach Algebras

Volker Runde
Amenable Banach Algebras Book PDF

Author : Volker Runde
Publisher : Springer Nature
Page : 468 pages
File Size : 54,5 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9781071603512

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Amenable Banach Algebras by Volker Runde Pdf

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.

Amenability of Discrete Groups by Examples

Kate Juschenko
Amenability of Discrete Groups by Examples Book PDF

Author : Kate Juschenko
Publisher : American Mathematical Society
Page : 180 pages
File Size : 43,5 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781470470326

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Amenability of Discrete Groups by Examples by Kate Juschenko Pdf

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

Function Spaces

Krzysztof Jarosz
Function Spaces Book PDF

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 44,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832691

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Function Spaces by Krzysztof Jarosz Pdf

This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $Lp$-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented.

Function Spaces in Modern Analysis

Krzysztof Jarosz
Function Spaces in Modern Analysis Book PDF

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 256 pages
File Size : 52,5 Mb
Release : 2011-07-18
Category : Mathematics
ISBN : 9780821852514

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Function Spaces in Modern Analysis by Krzysztof Jarosz Pdf

This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Banach Algebras and Their Applications

Anthony To-Ming Lau,Volker Runde
Banach Algebras and Their Applications Book PDF

Author : Anthony To-Ming Lau,Volker Runde
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 43,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834718

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Banach Algebras and Their Applications by Anthony To-Ming Lau,Volker Runde Pdf

This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

The Second Duals of Beurling Algebras

Harold G. Dales,Anthony To-Ming Lau
The Second Duals of Beurling Algebras Book PDF

Author : Harold G. Dales,Anthony To-Ming Lau
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 44,6 Mb
Release : 2005
Category : Banach algebras
ISBN : 9780821837740

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The Second Duals of Beurling Algebras by Harold G. Dales,Anthony To-Ming Lau Pdf

Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.

Combinatorial Set Theory of C*-algebras

Ilijas Farah
Combinatorial Set Theory of C algebras Book PDF

Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 47,6 Mb
Release : 2019-12-24
Category : Mathematics
ISBN : 9783030270933

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Combinatorial Set Theory of C*-algebras by Ilijas Farah Pdf

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Operator Algebras and Their Modules

David P. Blecher,Christian Le Merdy
Operator Algebras and Their Modules Book PDF

Author : David P. Blecher,Christian Le Merdy
Publisher : Oxford University Press
Page : 128 pages
File Size : 42,5 Mb
Release : 2004-10-07
Category : Mathematics
ISBN : 9780191523564

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Operator Algebras and Their Modules by David P. Blecher,Christian Le Merdy Pdf

This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, nonselfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important noncommutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

Recent Progress in Functional Analysis

K.D. Bierstedt,J. Bonet,Anna Maestre,J. Schmets
Recent Progress in Functional Analysis Book PDF

Author : K.D. Bierstedt,J. Bonet,Anna Maestre,J. Schmets
Publisher : Elsevier
Page : 469 pages
File Size : 55,5 Mb
Release : 2001-09-20
Category : Mathematics
ISBN : 9780080515922

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Recent Progress in Functional Analysis by K.D. Bierstedt,J. Bonet,Anna Maestre,J. Schmets Pdf

This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.

Ten Lectures on Cognitive Semantics

Leonard Talmy
Ten Lectures on Cognitive Semantics Book PDF

Author : Leonard Talmy
Publisher : BRILL
Page : 474 pages
File Size : 50,8 Mb
Release : 2018-01-29
Category : Language Arts & Disciplines
ISBN : 9789004349575

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Ten Lectures on Cognitive Semantics by Leonard Talmy Pdf

In his ten Beijing lectures, Leonard Talmy represents the range of his work in cognitive semantics. This approach concerns the linguistic representation of conceptual structure: the patterns in which and processes by which conceptual content is organized in language.

Mathematical Theory of Feynman Path Integrals

Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi
Mathematical Theory of Feynman Path Integrals Book PDF

Author : Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi
Publisher : Springer
Page : 182 pages
File Size : 48,7 Mb
Release : 2008-05-06
Category : Mathematics
ISBN : 9783540769569

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Mathematical Theory of Feynman Path Integrals by Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi Pdf

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Mathematical Models of Granular Matter

Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano
Mathematical Models of Granular Matter Book PDF

Author : Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 44,7 Mb
Release : 2008-04-18
Category : Technology & Engineering
ISBN : 9783540782766

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Mathematical Models of Granular Matter by Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano Pdf

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Mathematical Epidemiology

Fred Brauer,Pauline van den Driessche,J. Wu
Mathematical Epidemiology Book PDF

Author : Fred Brauer,Pauline van den Driessche,J. Wu
Publisher : Springer
Page : 414 pages
File Size : 52,8 Mb
Release : 2008-04-13
Category : Medical
ISBN : 9783540789116

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Mathematical Epidemiology by Fred Brauer,Pauline van den Driessche,J. Wu Pdf

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).