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2016 | OriginalPaper | Buchkapitel

4. Ultraproducts of Type \(\mathcal{L}_{\infty }\)

verfasst von : Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno

Erschienen in: Separably Injective Banach Spaces

Verlag: Springer International Publishing

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Abstract

The Banach space ultraproduct construction is perhaps the main bridge between model theory and the theory of Banach spaces and its ramifications. Ultraproducts of Banach spaces, even at a very elementary level, proved very useful in local theory, the study of Banach lattices, and also in several nonlinear problems, such as the uniform and Lipschitz classification of Banach spaces. We refer the reader to Heinrich’s survey paper [126] and Sims’ notes [234] for two complementary accounts. Traditionally, the main investigations about Banach space ultraproducts have focused on the isometric theory, reaching a quite coherent set of results very early, as can be seen in [132]. We will review some results on the isometric theory of ultraproducts in Sect. 4.7.4, but most of the Chapter is placed in the isomorphic context.

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Titel: Ultraproducts of Type
verfasst von: Antonio Avilés
Félix Cabello Sánchez
Jesús M. F. Castillo
Manuel González
Yolanda Moreno
Verlag: Springer International Publishing
Buch: Separably Injective Banach Spaces
Print ISBN: 978-3-319-14740-6

Electronic ISBN: 978-3-319-14741-3

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-14741-3_4

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