Banach spaces of universal disposition

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class M of normed spaces. The method produces, among others, the only separable Banach space of almost-universal disposition with respect to the class F of finite-dimension...

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Bibliographic Details
Published in:Journal of functional analysis 2011-11, Vol.261 (9), p.2347-2361
Main Authors: Avilés, Antonio, Cabello Sánchez, Félix, Castillo, Jesús M.F., González, Manuel, Moreno, Yolanda
Format: Article
Language:English
Subjects:
Banach spaces
Isometric embedding
Separable injectivity
Universal disposition
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Summary:In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class M of normed spaces. The method produces, among others, the only separable Banach space of almost-universal disposition with respect to the class F of finite-dimensional spaces (Gurariĭ space G ); or the only, under CH, Banach space with density character the continuum which is of universal disposition with respect to the class S of separable spaces (Kubis space K ). We moreover show that K is isomorphic to an ultrapower of the Gurariĭ space and that it is not isomorphic to a complemented subspace of any C ( K ) -space. Other properties of spaces of universal disposition are also studied: separable injectivity, partially automorphic character and uniqueness.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2011.06.011