Homological Methods in Banach Space Theory
Homological Methods in Banach Space Theory
Jesús M. F. Castillo, Universidad de Extremadura, Spain
£69.99
GBPMany 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.
- The first book presenting a comprehensive step-by-step approach to homological methods in Banach space theory
- Includes many results old and recent that have never appeared in book form
- Reworks in context deep results taken from about fifty papers of Kalton
- Presents solutions to classical problems of functional analysis and formulates many new open problems for future research
Reviews & endorsements
'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
'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
Product details
January 2023Hardback
9781108478588
500 pages
235 × 158 × 39 mm
0.98kg
Available
Table of Contents
- Preliminaries
- 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.
