Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces write by Joram Lindenstrauss. This book was released on 2012-02-26. Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces available in PDF, EPUB and Kindle. 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.
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces write by Joram Lindenstrauss. This book was released on 2012-02-26. Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces available in PDF, EPUB and Kindle. 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.
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces write by Joram Lindenstrauss. This book was released on 1940. Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces available in PDF, EPUB and Kindle.
Lipschitz Functions
Lipschitz Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lipschitz Functions write by Ştefan Cobzaş. This book was released on 2019-05-23. Lipschitz Functions available in PDF, EPUB and Kindle. The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Open Problems in the Geometry and Analysis of Banach Spaces
Open Problems in the Geometry and Analysis of Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Open Problems in the Geometry and Analysis of Banach Spaces write by Antonio J. Guirao. This book was released on 2016-07-26. Open Problems in the Geometry and Analysis of Banach Spaces available in PDF, EPUB and Kindle. This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.
