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Spaces of Universal Disposition

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Separably Injective Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2132))

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Abstract

In this chapter we deal with Banach spaces of universal disposition and almost universal disposition. These notions were introduced in the sixties by Gurariy, who constructed the (unique, up to isometries) separable Banach space of almost universal disposition for finite dimensional spaces in [118]. Spaces of universal disposition for separable Banach spaces are interesting for us because they are 1-separably injective (Theorem 3.5). More yet, the only way we know of obtaining separably injective p-Banach spaces is to construct p-Banach spaces of universal disposition (see Sect. 3.4.3).

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Authors and Affiliations

  1. Dpto. de Matemáticas, Universidad de Murcia, Murcia, Spain

    Antonio Avilés

  2. Dpto. de Matemáticas, Universidad de Extremadura, Badajoz, Spain

    Félix Cabello Sánchez & Jesús M. F. Castillo

  3. Dpto. de Matemáticas, Universidad de Cantabria, Santander, Spain

    Manuel González

  4. Dpto. de Matemáticas, Universidad de Extremadura, Cáceres, Spain

    Yolanda Moreno

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  1. Antonio Avilés
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  2. Félix Cabello Sánchez
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  3. Jesús M. F. Castillo
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  4. Manuel González
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  5. Yolanda Moreno
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Avilés, A., Sánchez, F.C., Castillo, J.M.F., González, M., Moreno, Y. (2016). Spaces of Universal Disposition. In: Separably Injective Banach Spaces. Lecture Notes in Mathematics, vol 2132. Springer, Cham. https://doi.org/10.1007/978-3-319-14741-3_3

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