Separably Injective Banach Spaces

By A. Avilés, F. C. Sánchez, J. Castillo, Manuel González, Yolanda Moreno. 2011

111 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/89fd5283b6ff296c12f9635fd2f5e0bfadc64493

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  1. A. Avilés
  2. F. Cabello
  3. J. Castillo
  4. Manuel González
  5. Yolanda Moreno

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