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
16 - Tensor Products
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
This is a short introduction to the basics of the theory of normed tensor products. The m-fold tensor product of linear spaces is defined through the universal property. If the involved spaces are normed, then the projective and injective norms on the tensor product are. Basic properties are given: the metric mapping property and their relationship with continuous linear mappings. The symmetric m-fold tensor product and the symmetric projective and injective norms are defined analogously. These are related to the m-homogeneous polynomials.
Keywords
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- Chapter
- Information
- Dirichlet Series and Holomorphic Functions in High Dimensions , pp. 410 - 434Publisher: Cambridge University PressPrint publication year: 2019