Banach Spaces And Descriptive Set Theory Selected Topics
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Banach Spaces And Descriptive Set Theory Selected Topics
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Author : Pandelis Dodos
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-10
Banach Spaces And Descriptive Set Theory Selected Topics written by Pandelis Dodos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-10 with Mathematics categories.
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.
Descriptive Topology In Selected Topics Of Functional Analysis
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Author : Jerzy Kąkol
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-30
Descriptive Topology In Selected Topics Of Functional Analysis written by Jerzy Kąkol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Mathematics categories.
"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.
Fr Chet Differentiability Of Lipschitz Functions And Porous Sets In Banach Spaces Am 179
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Author : Joram Lindenstrauss
language : en
Publisher: Princeton University Press
Release Date : 2012-02-26
Fr Chet Differentiability Of Lipschitz Functions And Porous Sets In Banach Spaces Am 179 written by Joram Lindenstrauss and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-26 with Mathematics categories.
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.
Recent Progress In General Topology Iii
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Author : K.P. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Recent Progress In General Topology Iii written by K.P. Hart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Topics In Algebraic And Topological K Theory
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Author : Paul Frank Baum
language : en
Publisher: Springer
Release Date : 2010-10-28
Topics In Algebraic And Topological K Theory written by Paul Frank Baum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-28 with Mathematics categories.
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Homological Methods In Banach Space Theory
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Author : Félix Cabello Sánchez
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-31
Homological Methods In Banach Space Theory written by Félix Cabello Sánchez and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-31 with Mathematics categories.
Approaches Banach space theory using methods from homological algebra, with concrete examples and proofs of many new and classical results.
Some Mathematical Models From Population Genetics
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Author : Alison Etheridge
language : en
Publisher: Springer
Release Date : 2011-01-05
Some Mathematical Models From Population Genetics written by Alison Etheridge and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-05 with Mathematics categories.
This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
Lebesgue And Sobolev Spaces With Variable Exponents
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Author : Lars Diening
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31
Lebesgue And Sobolev Spaces With Variable Exponents written by Lars Diening and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Mathematics categories.
The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Geometry Of Banach Spaces Selected Topics
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Author : J. Diestel
language : en
Publisher: Springer
Release Date : 2006-11-14
Geometry Of Banach Spaces Selected Topics written by J. Diestel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Topics In Banach Space Theory
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Author : Fernando Albiac
language : en
Publisher: Springer
Release Date : 2016-07-19
Topics In Banach Space Theory written by Fernando Albiac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-19 with Mathematics categories.
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