Homological Methods in Banach Space Theory

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.

List 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.

About the author

Félix Cabello Sánchez is Professor of Mathematics at the Universidad de Extremadura. He is co-author of the monograph Separably Injective Banach Spaces (2016).Jesús M. F. Castillo is Professor of Mathematics at the Universidad de Extremadura. He is co-author of the monographs Three-space Problems in Banach Space Theory (1997) and Separably Injective Banach Spaces (2016).

Summary

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.

Product details

• Authors: Felix (Universidad De Extremadura Cabello Sanchez, Félix Cabello Sánchez, Jesús M F Castillo, Jesús M. F. Castillo, Jesus M. F. (Universidad de Extremadura Castillo
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.12.2022
• EAN: 9781108478588
• ISBN: 978-1-108-47858-8
• No. of pages: 500
• Series: Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Mathematical Analysis, Numerical analysis, Functional analysis & transforms, Functional analysis and transforms