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Separably Injective Banach Spaces

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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

It is no exaggeration to say that the theory of separably injective spaces is quite different from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in the main topic of the monograph, namely, separably injective spaces and their “universal” version. After giving the main definitions and taking a look at the first natural examples one encounters, we present the basic characterizations and a number of structural properties of (universally) separable injective Banach spaces. We will show, among other things, that 1-separably injective spaces are not necessarily isometric to C-spaces, that (universally) separably injective spaces are not necessarily complemented in any C-space—the separably injective part of the assertion will be shown here while the “universal” part can be found in the next chapter—and that there exist essential differences between 1-separably injective and 2-separably injective spaces.

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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). Separably Injective Banach Spaces. In: Separably Injective Banach Spaces. Lecture Notes in Mathematics, vol 2132. Springer, Cham. https://doi.org/10.1007/978-3-319-14741-3_2

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