Geodesic
A Note on Relatively Injective $C_0(S)$-Modules $C_0(S)$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 4, pp. 55-62

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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 $s\in S$.
Keywords: injective Banach module, $C_0(S)$-space, almost compact space. 
@article{FAA_2021_55_4_a3,
     author = {N. T. Nemesh},
     title = {A {Note} on {Relatively} {Injective} $C_0(S)${-Modules} $C_0(S)$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {55--62},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2021_55_4_a3/}
}
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N. T. Nemesh. A Note on Relatively Injective $C_0(S)$-Modules $C_0(S)$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 4, pp. 55-62. http://geodesic.mathdoc.fr/item/FAA_2021_55_4_a3/