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Cambridge Studies in Advanced Mathematics Ser.: Homological Methods in Banach Space Theory by Félix Cabello Sánchez and Jesús M. F. Castillo (2023, Hardcover)

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Homological Methods in Banach Space Theory, Hardcover by Sánchez, Félix Cabello; Castillo, Jesu´s M. F., ISBN 1108478581, ISBN-13 9781108478588, Brand New, Free shipping in the US

About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101108478581

ISBN-139781108478588

eBay Product ID (ePID)18058372302

Product Key Features

Number of Pages500 Pages

Publication NameHomological Methods in Banach Space Theory

LanguageEnglish

Publication Year2023

SubjectGeneral, Mathematical Analysis

TypeTextbook

AuthorFélix Cabello Sánchez, Jesús M. F. Castillo

Subject AreaMathematics

SeriesCambridge Studies in Advanced Mathematics Ser.

FormatHardcover

Dimensions

Item Height1.5 in

Item Length9.3 in

Item Width6.2 in

Additional Product Features

Intended AudienceScholarly & Professional

Dewey Edition23

Reviews'Commutative diagrams are a natural and concise method of encoding information about various mathematical objects, and they deserve to better known. Together with other categorical constructions such as ultrapowers, pullbacks and pushouts, they provide a big picture view and a framework for further progress. This book gives a comprehensive account of the applications of such techniques to numerous aspects of Banach spaces.' David Yost, Federation University, 'This masterpiece seemingly is an excellent math book saturated with lush insights and marvellous perspectives on Banach spaces. But start to read it. When furniture and people start to appear to you as diagrams you will realize that you are in the middle of a fascinating wildlife event.' Piotr Koszmider, Institute of Mathematics of the Polish Academy of Sciences, 'This comprehensive treatment of Homological Methods in Banach Space Theory by two authors who are among the most adept at using algebraic tools in functional analysis is a must for every mathematician who is interested in the geometry of Banach spaces.' William B. Johnson, Texas A&M University

Series Volume NumberSeries Number 203

IllustratedYes

Dewey Decimal515.732

Table Of ContentPreliminaries; 1. Complemented subspaces of Banach spaces; 2. The language of homology; 3. Quasilinear maps; 4. The functor Ext and the homology sequences; 5. Local methods in the theory of twisted sums; 6. Fraissé limits by the pound; 7. Extensions of operators, isomorphisms and isometries; 8. Extension of C(K)-valued operators; 9. Singular exact sequences; 10. Back to Banach space theory; Bibliography; Index.

SynopsisMany 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., This book gives functional analysts a new perspective on their field and new tools to tackle its problems. It presents and explain many powerful results from the last half century and uses them to solve classical and new results in the theory of (quasi-) Banach spaces, while introducing the algebraic techniques from scratch with concrete examples.

LC Classification NumberQA322.2