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Author : Vitali D. Milman
Publisher :
ISBN 13 : 9783662184769
Total Pages : 172 pages
Book Rating : 4.1/5 (847 download)
Download or read book Asymptotic Theory of Finite Dimensional Normed Spaces written by Vitali D. Milman and published by . This book was released on 2014-01-15 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vitali D. Milman
Publisher : Springer
ISBN 13 : 3540388222
Total Pages : 166 pages
Book Rating : 4.5/5 (43 download)
Download or read book Asymptotic Theory of Finite Dimensional Normed Spaces written by Vitali D. Milman and published by Springer. This book was released on 2009-02-27 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].
Author :
Publisher : Elsevier
ISBN 13 : 9780080533506
Total Pages : 870 pages
Book Rating : 4.5/5 (335 download)
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Author : Shiri Artstein-Avidan
Publisher : American Mathematical Soc.
ISBN 13 : 1470421933
Total Pages : 451 pages
Book Rating : 4.4/5 (74 download)
Download or read book Asymptotic Geometric Analysis, Part I written by Shiri Artstein-Avidan and published by American Mathematical Soc.. This book was released on 2015-06-18 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.
Author : Monika Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 1461464064
Total Pages : 402 pages
Book Rating : 4.4/5 (614 download)
Download or read book Asymptotic Geometric Analysis written by Monika Ludwig and published by Springer Science & Business Media. This book was released on 2013-03-27 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.
Author : Vitali D. Milman
Publisher : Springer
ISBN 13 : 3540444890
Total Pages : 306 pages
Book Rating : 4.5/5 (44 download)
Download or read book Geometric Aspects of Functional Analysis written by Vitali D. Milman and published by Springer. This book was released on 2004-08-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.
Author : Guillaume Aubrun
Publisher : American Mathematical Soc.
ISBN 13 : 1470434687
Total Pages : 414 pages
Book Rating : 4.4/5 (74 download)
Download or read book Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory written by Guillaume Aubrun and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.
Author : Joram Lindenstrauss
Publisher : Springer
ISBN 13 : 3540392351
Total Pages : 296 pages
Book Rating : 4.5/5 (43 download)
Download or read book Geometric Aspects of Functional Analysis written by Joram Lindenstrauss and published by Springer. This book was released on 2006-11-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third published volume of the proceedings of the Israel Seminar on Geometric Aspects of Functional Analysis. The large majority of the papers in this volume are original research papers. There was last year a strong emphasis on classical finite-dimensional convexity theory and its connection with Banach space theory. In recent years, it has become evident that the notions and results of the local theory of Banach spaces are useful in solving classical questions in convexity theory. The present volume contributes to clarifying this point. In addition this volume contains basic contributions to ergodic theory, invariant subspace theory and qualitative differential geometry.
Author : Fernando Albiac
Publisher : Springer
ISBN 13 : 3319315579
Total Pages : 508 pages
Book Rating : 4.3/5 (193 download)
Download or read book Topics in Banach Space Theory written by Fernando Albiac and published by Springer. This book was released on 2016-07-19 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews
Author : Bor-Luh Lin
Publisher : American Mathematical Soc.
ISBN 13 : 0821851578
Total Pages : 201 pages
Book Rating : 4.8/5 (218 download)
Download or read book Banach Spaces written by Bor-Luh Lin and published by American Mathematical Soc.. This book was released on 1993 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Banach Space Theory, held at the Universidad de Los Andes in Merida, Venezuela in January 1992. These refereed papers contain the newest results in Banach space theory, real or complex function spaces, and nonlinear functional analysis. There are several excellent survey papers, including ones on homogeneous Banach spaces and applications of probability inequalities, in addition to an important research paper on the distortion problem. This volume is notable for the breadth of the mathematics presented.
Author : Silouanos Brazitikos
Publisher : American Mathematical Soc.
ISBN 13 : 1470414562
Total Pages : 618 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometry of Isotropic Convex Bodies written by Silouanos Brazitikos and published by American Mathematical Soc.. This book was released on 2014-04-24 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Author : Simon Donaldson
Publisher : Springer Science & Business Media
ISBN 13 : 030648658X
Total Pages : 424 pages
Book Rating : 4.3/5 (64 download)
Download or read book Different Faces of Geometry written by Simon Donaldson and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvath (USA) and Z. Szabo (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvath and Szabo). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun.Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Kahler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the 11/8 conjecture. LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even well-known 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the geometry is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra.The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems. - From the Preface by the Editors
Author :
Publisher : Cambridge University Press
ISBN 13 : 0521408504
Total Pages : 288 pages
Book Rating : 4.5/5 (214 download)
Download or read book Geometry of Banach Spaces written by and published by Cambridge University Press. This book was released on 1990 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 9780521655774
Total Pages : 260 pages
Book Rating : 4.6/5 (557 download)
Download or read book Linear Analysis written by Béla Bollobás and published by Cambridge University Press. This book was released on 1999-03-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated introduction to functional analysis.
Author : Bo'az Klartag
Publisher : Springer
ISBN 13 : 3319452827
Total Pages : 366 pages
Book Rating : 4.3/5 (194 download)
Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer. This book was released on 2017-04-17 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.
Author : Peter G. Casazza
Publisher : Springer
ISBN 13 : 3540460691
Total Pages : 212 pages
Book Rating : 4.5/5 (44 download)
Download or read book Tsirelson's Space written by Peter G. Casazza and published by Springer. This book was released on 2006-11-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).
Author : Noga Alon
Publisher : Springer Science & Business Media
ISBN 13 : 3034604254
Total Pages : 528 pages
Book Rating : 4.0/5 (346 download)
Download or read book Visions in Mathematics written by Noga Alon and published by Springer Science & Business Media. This book was released on 2011-04-22 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future.
