Banach spaces of universal disposition
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- 作者：Antonio ; Avilé ; s<sup>asup><sup> ; ; sup><sup>avileslo@um.essup> ; Fé ; lix ; Cabello Sá ; nchez<sup>bsup><sup> ; ; sup><sup>fcabello@unex.essup> ; Jesú ; s M.F. ; Castillo<sup>bsup><sup> ; ; sup><sup>castillo@unex.essup> ; Manuel ; Gonzá ; lez<sup>csup><sup> ; ; sup><sup>manuel.gonzalez@unican.essup> ; Yolanda ; Moreno<sup>dsup><sup> ; ; sup><sup>ymoreno@unex.essup>
- 关键词：Banach spaces ; Isometric embedding ; Universal disposition ; Separable injectivity
- 刊名：Journal of Functional Analysis
- 出版年：2011
- 出版时间：1 November 2011
- 年：2011
- 卷：261
- 期：9
- 页码：2347-2361
- 全文大小：177 K
文摘
In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class of normed spaces. The method produces, among others, the only separable Banach space of almost-universal disposition with respect to the class of finite-dimensional spaces (Gurari? space ); or the only, under CH, Banach space with density character the continuum which is of universal disposition with respect to the class of separable spaces (Kubis space ). We moreover show that is isomorphic to an ultrapower of the Gurari? space and that it is not isomorphic to a complemented subspace of any -space. Other properties of spaces of universal disposition are also studied: separable injectivity, partially automorphic character and uniqueness.