Homological Methods In Banach Space Theory

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Homological Methods In Banach Space Theory

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Author : Félix Cabello Sánchez
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-26

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 2023-01-26 with Mathematics categories.

Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.

Methods In Banach Space Theory

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Author : Jesus M. F. Castillo
language : en
Publisher: Cambridge University Press
Release Date : 2006-11-30

Methods In Banach Space Theory written by Jesus M. F. Castillo 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 2006-11-30 with Mathematics categories.

A comprehensive overview of modern Banach space theory.

Methods In Banach Space Theory

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Author : Jesús M. F. Castillo
language : en
Publisher:
Release Date : 2006

Methods In Banach Space Theory written by Jesús M. F. Castillo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Banach spaces categories.

This book presents an overview of modern Banach space theory. It contains sixteen papers that reflect the wide expanse of the subject. Articles are gathered into five sections according to methodology rather than the topics considered. The sections are: geometrical methods; homological methods; topological methods; operator theoretic methods; and also function space methods. Each section contains survey and research papers describing the state-of-the-art in the topic considered as well as some of the latest most important results. Researchers working in Banach space theory, functional analysis or operator theory will find much of interest here.

Banach Spaces And Their Applications In Analysis

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Author : Beata Randrianantoanina
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22

Banach Spaces And Their Applications In Analysis written by Beata Randrianantoanina and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.

In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.

Optimal Mass Transport On Euclidean Spaces

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Author : Francesco Maggi
language : en
Publisher: Cambridge University Press
Release Date : 2023-11-16

Optimal Mass Transport On Euclidean Spaces written by Francesco Maggi 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 2023-11-16 with Mathematics categories.

A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.

The Geometry Of Cubic Hypersurfaces

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-29

The Geometry Of Cubic Hypersurfaces written by Daniel Huybrechts 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 2023-06-29 with Mathematics categories.

A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.

Geometric Inverse Problems

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Author : Gabriel P. Paternain
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05

Geometric Inverse Problems written by Gabriel P. Paternain 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 2023-01-05 with Mathematics categories.

This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.

Algebraic Groups And Number Theory

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Author : Vladimir Petrovich Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory written by Vladimir Petrovich Platonov 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 2023-09-07 with Mathematics categories.

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Algebraic Groups And Number Theory Volume 1

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Author : Vladimir Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory Volume 1 written by Vladimir Platonov 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 2023-09-07 with Mathematics categories.

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Equivariant Cohomology In Algebraic Geometry

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Author : David Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-26

Equivariant Cohomology In Algebraic Geometry written by David Anderson 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 2023-10-26 with Mathematics categories.

A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.