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Banach space theory : the basis for linear and nonlinear analysis /
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space the...
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| Format: | Printed Book |
| Language: | English |
| Published: |
New York :
Springer,
c2011.
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| Series: | CMS books in mathematics.
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| Subjects: |
Table of Contents:
- Basic concepts in Banach spaces
- Hahn-Banach and Banach open mapping theorems
- Weak topologies and Banach spaces
- Schauder bases
- Structure of Banach spaces
- Finite-dimensional spaces
- Optimization
- C¹-smoothness in separable spaces
- Superreflexive spaces
- Higher order smoothness
- Dentability and differentiability
- Basics in nonlinear geometric analysis
- Weakly compactly generated spaces
- Topics in weak topologies on Banach spaces
- Compact operators on Banach spaces
- Tensor products
- Appendix: Basics in topology
- Nets and filters
- Nets and filters in topological spaces
- Ultraproducts
- The order topology on the ordinals
- Continuity of set-valued mappings
- The cantor space
- Baire's great theorem
- Polish spaces
- Uniform spaces
- Nets and filters in uniform spaces
- Partitions of unity
- Measure and integral
- Continued fractions and the representation of the irrational numbers.