Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- 14 Selected Topics on Banach Space Theory
- 15 Infinite Dimensional Holomorphy
- 16 Tensor Products
- 17 Probabilistic Tools II
- Part 3 Replacing Polydiscs by Other Balls
- Part 4 Vector-Valued Aspects
- References
- Symbol Index
- Subject Index
14 - Selected Topics on Banach Space Theory
from Part 2 - Advanced Toolbox
Published online by Cambridge University Press: 19 July 2019
Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- 14 Selected Topics on Banach Space Theory
- 15 Infinite Dimensional Holomorphy
- 16 Tensor Products
- 17 Probabilistic Tools II
- Part 3 Replacing Polydiscs by Other Balls
- Part 4 Vector-Valued Aspects
- References
- Symbol Index
- Subject Index
Summary
Basic topics on Banach space theory needed for the text are reviewed. Hahn-Banach theorem, Baire’s theorem, uniform boundedness principle, closed graph theorem, weak topologies, Banach-Alaoglu theorem, unconditional basis, Banach sequence spaces, summing operators, factorable operators, cotype, Kahane inequality.
Keywords
- Type
- Chapter
- Information
- Dirichlet Series and Holomorphic Functions in High Dimensions , pp. 339 - 350Publisher: Cambridge University PressPrint publication year: 2019