Generalized injectivity of Banach modules

Abstract

In this paper, we study the notion of $\varphi$-injectivity in the special case that $\varphi =0$. For an arbitrary locally compact group $G$, we characterize the 0-injectivity of $L^1(G)$ as a left $L^1(G)$ module. Also, we show that $L^1(G{)}^{\ast \ast }$ and $L^p(G)$ for $1<p<\infty$ are 0-injective Banach $L^1(G)$ modules.

8 pages