Abstract
To put in a proper context the results in this monograph it will be useful to keep in mind the theory of injective spaces and the general theory of \(\mathcal{L}_{\infty }\)-spaces. In this way one can compare the stability properties and the variety of examples of separably injective spaces that will be presented later with those of injective spaces. For the convenience of the reader, in this preparatory chapter we have summarized the basic properties and examples of injective Banach spaces, as well as a few remarkable examples of non-injective spaces, and some criteria that allow one to check whether a space is or is not injective. The results in this chapter have been known for many years and thus proofs will be sketched or omitted. For alternative expositions we refer to [1, Sect. 4.3], [83, Appendix D], [194, Sects. 7–9] and [253, Sect. 2].
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Avilés, A., Sánchez, F.C., Castillo, J.M.F., González, M., Moreno, Y. (2016). A Primer on 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_1
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