Renormings in Banach spaces : a toolbox / Antonio José Guirao, Vicente Montesinos, Václav Zizler.
Guirao, Antonio J.; Montesinos Julve, Vicente.; Zizler, Vaclav.
2022
QA322.2
Available Online

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Title Renormings in Banach spaces : a toolbox / Antonio José Guirao, Vicente Montesinos, Václav Zizler.
Author Guirao, Antonio J.
ISBN 9783031086557 (electronic bk.)
3031086554 (electronic bk.)
9783031086540
3031086546
DOI https://doi.org/10.1007/978-3-031-08655-7
Publication Details Cham : Springer, 2022.
Language English
Description 1 online resource (621 pages)
Item Number 10.1007/978-3-031-08655-7 doi
Call Number QA322.2
Dewey Decimal Classification 515/.732
Summary 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 equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed September 1, 2022).
Added Author Montesinos Julve, Vicente.
Zizler, Vaclav.
Series Monografie matematyczne ; v. 75.
Available in Other Form Renormings in Banach Spaces
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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 Smulyans 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 Tsirelsons 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 Fabians farm of Lipschitz Asplund spaces
27 Fonfs land of spaces isomorphic to polyhedral spaces
28 Hajeks 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.

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