A characterization of norm compactness in the Bochner space Lp(G;B) for an arbitrary locally compact group G

In this paper, we generalize a result of N. Dinculeanu which characterizes norm compactness in the Bochner space Lp(G;B) in terms of an approximate identity and translation operators, where G is a locally compact abelian group and B is a Banach space. Our characterization includes the case where G is nonabelian, and we weaken the hypotheses on the approximate identity used, providing new results even for the case B=C and G=Rn.