Download or read book Multipliers and Approximation Properties of Groups written by Ignacio Vergara Soto and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focusses on some approximation properties which generalise amenability for locally compact groups. These properties are defined by means of multipliers of certain algebras associated to the groups. The first part is devoted to the study of the p-AP, which is an extension of the AP of Haagerup and Kraus to the context of operators on Lp spaces. The main result asserts that simple Lie groups of higher rank and finite centre do not satisfy p-AP for any p between 1 and infinity. The second part concentrates on radial Schur multipliers on graphs. The study of these objects is motivated by some connections with actions of discrete groups and weak amenability. The three main results give necessary and sufficient conditions for a function of the natural numbers to define a radial multiplier on different classes of graphs generalising trees. More precisely, the classes of graphs considered here are products of trees, products hyperbolic graphs and finite dimensional CAT(0) cube complexes.
Download or read book C algebras and Elliptic Theory written by Bogdan Bojarski and published by Springer Science & Business Media. This book was released on 2006-11-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
Download or read book textrm C Algebras and Finite Dimensional Approximations written by Nathanial Patrick Brown and published by American Mathematical Soc.. This book was released on 2008 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: $\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.
Download or read book Lectures on Coarse Geometry written by John Roe and published by American Mathematical Soc.. This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
Download or read book Tensor Products of C algebras and Operator Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2020-02-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Download or read book Riesz Transforms Hodge Dirac Operators and Functional Calculus for Multipliers written by Cédric Arhancet and published by Springer Nature. This book was released on 2022-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
Download or read book Banach Algebras and Their Applications written by Anthony To-Ming Lau and published by American Mathematical Soc.. This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Banach Function Algebras Arens Regularity and BSE Norms written by Harold Garth Dales and published by Springer Nature. This book was released on with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier and Fourier Stieltjes Algebras on Locally Compact Groups written by Eberhard Kaniuth and published by American Mathematical Soc.. This book was released on 2018-07-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1985-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Banach Algebras and Applications written by Mahmoud Filali and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Issues in Calculus Mathematical Analysis and Nonlinear Research 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Calculus, Mathematical Analysis, and Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Calculus, Mathematical Analysis, and Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Groups Geometry and Dynamics written by and published by . This book was released on 2007 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. Covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.
Download or read book An Introduction to the Theory of Multipliers written by Ronald Larsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: When I first considered writing a book about multipliers, it was my intention to produce a moderate sized monograph which covered the theory as a whole and which would be accessible and readable to anyone with a basic knowledge of functional and harmonic analysis. I soon realized, however, that such a goal could not be attained. This realization is apparent in the preface to the preliminary version of the present work which was published in the Springer Lecture Notes in Mathematics, Volume 105, and is even more acute now, after the revision, expansion and emendation of that manuscript needed to produce the present volume. Consequently, as before, the treatment given in the following pages is eclectric rather than definitive. The choice and presentation of the topics is certainly not unique, and reflects both my personal preferences and inadequacies, as well as the necessity of restricting the book to a reasonable size. Throughout I have given special emphasis to the func tional analytic aspects of the characterization problem for multipliers, and have, generally, only presented the commutative version of the theory. I have also, hopefully, provided too many details for the reader rather than too few.
Download or read book American Journal of Mathematics written by and published by . This book was released on 1995 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Combinatorics with Applications to Mathematical Physics written by Anatoly M. Vershik and published by Springer. This book was released on 2003-07-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.
Download or read book Hypercontractivity in Group von Neumann Algebras written by Marius Junge and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).
