A Note on Relatively Injective $C_0(S)$-Modules $C_0(S)$

N. T. Nemesh

Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 4, pp. 55-62.

Résumé

In this note we discuss some necessary and some sufficient conditions for the relative injectivity of the $C_0(S)$-module $C_0(S)$, where $S$ is a locally compact Hausdorff space. We also give a Banach module version of Sobczyk's theorem. The main result of the paper is as follows: if the $C_0(S)$-module $C_0(S)$ is relatively injective, then $S=\beta(S\setminus \{s\})$ for any limit point $s\in S$.

Détail

Keywords: injective Banach module, $C_0(S)$-space, almost compact space.

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