This is an announcement for the paper "Banach spaces of universal disposition" by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno.
Abstract: In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\u{\i} space $\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\mathfrak F$ of finite dimensional spaces), or the Kubis space $\mathcal K$ (under {\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\sf CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties.
Archive classification: math.FA
Mathematics Subject Classification: 46A22, 46B04, 46B08, 46B26
Submitted from: castillo@unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.6065
or