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Banach Mazur Distances And Finite Dimensional Operator Ideals
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Book Synopsis Banach-Mazur Distances and Finite-dimensional Operator Ideals by : Nicole Tomczak-Jaegermann
Download or read book Banach-Mazur Distances and Finite-dimensional Operator Ideals written by Nicole Tomczak-Jaegermann and published by Longman Scientific and Technical. This book was released on 1989 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of the Geometry of Banach Spaces by : William B. Johnson
Download or read book Handbook of the Geometry of Banach Spaces written by William B. Johnson and published by Elsevier. This book was released on 2001 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
Book Synopsis Tensor Norms and Operator Ideals by : A. Defant
Download or read book Tensor Norms and Operator Ideals written by A. Defant and published by Elsevier. This book was released on 1992-11-26 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.
Book Synopsis Handbook of the Geometry of Banach Spaces by :
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 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Book Synopsis Asymptotic Theory of Finite Dimensional Normed Spaces by : Vitali D. Milman
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].
Book Synopsis Handbook of Convex Geometry by : Bozzano G Luisa
Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Book Synopsis Convexity and Concentration by : Eric Carlen
Download or read book Convexity and Concentration written by Eric Carlen and published by Springer. This book was released on 2017-04-20 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.
Book Synopsis Introduction to Operator Space Theory by : Gilles Pisier
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Book Synopsis Geometric Aspects of Functional Analysis by :
Download or read book Geometric Aspects of Functional Analysis written by and published by Springer Science & Business Media. This book was released on 2003 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Banach Space Theory by : Marián Fabian
Download or read book Banach Space Theory written by Marián Fabian and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Book Synopsis Applied Mathematics Reviews, Volume 1 by : George A Anastassiou
Download or read book Applied Mathematics Reviews, Volume 1 written by George A Anastassiou and published by World Scientific. This book was released on 2000-06-09 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world.This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.
Book Synopsis Applied Mathematics Reviews by : George A. Anastassiou
Download or read book Applied Mathematics Reviews written by George A. Anastassiou and published by World Scientific. This book was released on 2000 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world. This volume contains 14 high quality survey articles -- incorporating original results and describing the main research activities of contemporary applied mathematics -- written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.
Book Synopsis Probability in Banach Spaces by : Michel Ledoux
Download or read book Probability in Banach Spaces written by Michel Ledoux and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Book Synopsis Banach Spaces for Analysts by : P. Wojtaszczyk
Download or read book Banach Spaces for Analysts written by P. Wojtaszczyk and published by Cambridge University Press. This book was released on 1996-08 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be used with graduate courses in Banach space theory.
Book Synopsis Upper and Lower Bounds for Stochastic Processes by : Michel Talagrand
Download or read book Upper and Lower Bounds for Stochastic Processes written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2014-02-12 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.
Book Synopsis Theorems of the 21st Century by : Bogdan Grechuk
Download or read book Theorems of the 21st Century written by Bogdan Grechuk and published by Springer. This book was released on 2019-06-15 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.
