Book contents
- Frontmatter
- Contents
- Preface
- 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 Fraïssé Limits by the Pound
- 7 Extension of Operators, Isomorphisms and Isometries
- 8 Extension of C(K)-Valued Operators
- 9 Singular Exact Sequences
- 10 Back to Banach Space Theory
- Bibliography
- Index
Preliminaries
Published online by Cambridge University Press: 19 January 2023
- Frontmatter
- Contents
- Preface
- 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 Fraïssé Limits by the Pound
- 7 Extension of Operators, Isomorphisms and Isometries
- 8 Extension of C(K)-Valued Operators
- 9 Singular Exact Sequences
- 10 Back to Banach Space Theory
- Bibliography
- Index
Summary
Anyone familiar with $\ell_p$ spaces can follow a healthy 50 per cent of this book; if familiar with $L_p$ spaces, the percentage raises to 75 per cent. All the rest can be found in the text. Anyway, a reasonable list of prerequisites that could help a smooth reading would be some acquaintance with classical Banach space theory; lack of fear when local convexity disappears; a certain bias towards abstraction; calm when non-linear objects show off, and some fondness for exotic spaces. The reader is reminded in this chapter about notation for the book, sets and functions, Boolean algebras, ordinals and cardinals, compact spaces, quasinormed spaces and operators, classical spaces, approximation properties and operator ideals.
- Type
- Chapter
- Information
- Homological Methods in Banach Space Theory , pp. 1 - 8Publisher: Cambridge University PressPrint publication year: 2023