Download or read book Some Topological and Geometrical Structures in Banach Spaces written by Nassif Ghoussoub and published by American Mathematical Soc.. This book was released on 1987 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this memoir, we study the interrelations between the topological, measure theoretical and geometrical structures in certain classes of Banach spaces. The focus is on those spaces whose bounded subsets have arbitrarily norm-small convex combinations of slices. This class contains spaces with the Radon-Nikodym property as well as B-convex Banach spaces. The topological analysis leads to the concept of "first class functions around sets". This extension of the classical notion of Baire-1 functions is developed in a general non-linear setting.
Download or read book Some Topological and Geometrical Structures in Banach Spaces written by Nassif Ghoussoub and published by . This book was released on 1987 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Structure Topology and Symplectic Geometry written by Kamal Shah and published by BoD – Books on Demand. This book was released on 2021-04-07 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad overview of the theory and applications of structure topology and symplectic geometry. Over six chapters, the authors cover topics such as linear operators, Omega and Clifford algebra, and quasiconformal reflection across polygonal lines. The book also includes four interesting case studies on time series analysis in practice. Finally, it provides a snapshot of some current trends and future challenges in the research of symplectic geometry theory. Structure Topology and Symplectic Geometry is a resource for scholars, researchers, and teachers in the field of mathematics, as well as researchers and students in engineering.
Download or read book Banach Spaces and Descriptive Set Theory Selected Topics written by Pandelis Dodos and published by Springer Science & Business Media. This book was released on 2010-05-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
Download or read book Theory of Convex Structures written by M.L.J. van de Vel and published by Elsevier. This book was released on 1993-08-02 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.
Download or read book Geometric Nonlinear Functional Analysis written by Yoav Benyamini and published by American Mathematical Soc.. This book was released on 1998 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories. Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated.
Download or read book Biorthogonal Systems in Banach Spaces written by Petr Hajek and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
Download or read book Operator and Matrix Theory Function Spaces and Applications written by Marek Ptak and published by Springer Nature. This book was released on with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Martingales in Banach Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2016-06-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Download or read book Functional Analysis written by Edward W. Odell 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: The articles in this volume are based on talks given in a seminar at Austin during 1986-87. They range from those dealing with fresh research and discoveries to exposition and new proofs of older results. The main topics and themes include geometric and analytic properties of infinite-dimensional Banach spaces and their convex subsets as well as some aspects of Banach spaces associated with harmonic analysis and Banach algebras.
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2016-11-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Download or read book Introduction to Banach Spaces Analysis and Probability written by Daniel Li and published by Cambridge University Press. This book was released on 2018 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.
Download or read book Introduction to Banach Spaces Analysis and Probability Volume 1 written by Daniel Li and published by Cambridge University Press. This book was released on 2017-11-02 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.
Download or read book Functional Analysis written by Edward E., Jr. Odell and published by Springer. This book was released on 2006-11-14 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume yield a variety of powerful tools for penetrating the structure of Banach spaces, including the following topics: the structure of Baire-class one functions with Banach space applications, operator extension problems, the structure of Banach lattices tensor products of operators and Banach spaces, Banach spaces of certain classes of Fourier series, uniformly stable Banach spaces, the hyperplane conjecture for convex bodies, and applications of probability theory to local Banach space structure. With contributions by: R. Haydon, E. Odell, H. Rosenthal: On certain classes of Baire-1 functions with applications to Banach space theory.- K. Ball: Normed spaces with a weak-Gordon-Lewis property.- S.J. Szarek: On the geometry of the Banach-Mazur compactum.- P. Wojtaszczyk: Some remarks about the space of measures with uniformly bounded partial sums and Banach-Mazur distances between some spaces of polynomials.- N. Ghoussoub, W.B. Johnson: Operators which factor through Banach lattices not containing co.- W.B. Johnson, G. Schechtman: Remarks on Talagrand's deviation inequality for Rademacher functions.- M. Zippin: A Global Approach to Certain Operator Extension Problems.- H. Knaust, E. Odell: Weakly null sequences with upper lp-estimates.- H. Rosenthal, S.J. Szarek: On tensor products of operators from Lp to Lq.- T. Schlumprecht: Limited Sets in Injective Tensor Products.- F. Räbiger: Lower and upper 2-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices.- D.H. Leung: Embedding l1 into Tensor Products of Banach Spaces.- P. Hitczenko: A remark on the paper "Martingale inequalities in rearrangement invariant function spaces" by W.B. Johnson, G. Schechtman.- F. Chaatit: Twisted types and uniform stability.
Download or read book Banach Space Theory written by Bor-Luh Lin and published by American Mathematical Soc.. This book was released on 1989 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from a Research Workshop on Banach Space Theory held at the University of Iowa in Iowa City in July 1987. The workshop provided participants with a collaborative working atmosphere in which ideas could be exchanged informally. Several papers were initiated during the workshop and are presented here in their final form. Also included are contributions from several experts who were unable to attend the workshop. None of the papers will be published elsewhere. During the workshop, two hours each day were devoted to seminars on current problems in such areas as weak Hilbert spaces, zonoids, analytic martingales, and operator theory, and these topics are reflected in some of the papers in the collection.
Download or read book Seminar on Functional Analysis 1987 written by José Orihuela and published by EDITUM. This book was released on 1988 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
