Abstract of a paper by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel Gonzalez, and Yolanda Moreno
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 http://arXiv.org/abs/1103.6065
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