Renormings in Banach Spaces A Toolbox
This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalen...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Birkhäuser
2022, 2022
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| Edition: | 1st ed. 2022 |
| Series: | Monografie Matematyczne
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1 Norms, Normed spaces, Banach spaces
- 2 Some basic definitions and tools
- 3 Equivalent norms
- 4 Basic differentiability in Banach spaces
- 5 Basic convexity
- 6 Some structural properties of Banach spaces
- 7 The use of Smulyan’s tests
- 8 Asplund averaging I
- 9 Tools for renorming
- 10 Renorming of nonseparable Banach spaces
- 11 Examples on C1-smoothness
- 12 Examples on Rotundity
- 13 Nonlinear Transfer Techniques
- 14 Lipschitz functions
- 15 Spaces isomorphic to Hilbert spaces
- 16 Superreflexive spaces
- 17 The Kingdom of Tsirelson’s space
- 18 The L(infinity) spaces
- 19 Higher order smoothness
- 20 James boundaries
- 21 RNP property
- 22 SSD spaces
- 23 Norms with MIP
- 24 Nicely smooth Banach spaces
- 25 Weak Hadamard differentiability
- 26 Fabian’s farm of Lipschitz Asplund spaces
- 27 Fonf’s land of spaces isomorphic to polyhedral spaces
- 28 Hájek’s garden of nice functions on c0(gamma)
- 29 Kottman-type results
- 30 3-space properties
- 31 Polynomials
- 32 Miscellaneous applications
- 33 Miscellaneous topics
- 34 More on WCG spaces and their relatives
- 35 Valdivia compacta
- 36 Renorming classical spaces
- 37 Symmetric norms
- 38 A concise list of coordinates of the relationship
- 39 Some easily formulated open questions on construction of norms in separable spaces
- Index of figures