Abstract
Many of the results presented in this monograph about (universal) separable injectivity can be formulated in terms of the extension of operators with separable range. It is natural to attempt to obtain analogous results under more relaxed conditions in the size of the range of the operators. In this Chapter we consider the notions of (universal) \(\aleph\)-injectivity obtained by allowing domain or ranges of operators to have larger density characters. As we shall see, some results easily generalize to the higher cardinal context, some present many difficulties, and some are simply impossible. And, of course, cardinal assumptions are necessary.
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Avilés, A., Sánchez, F.C., Castillo, J.M.F., González, M., Moreno, Y. (2016). \(\aleph\)-Injectivity. In: Separably Injective Banach Spaces. Lecture Notes in Mathematics, vol 2132. Springer, Cham. https://doi.org/10.1007/978-3-319-14741-3_5
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DOI: https://doi.org/10.1007/978-3-319-14741-3_5
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