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 On the separating ideals of some vector-valued group algebras Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 737-746 Ramesh V. Garimella Tennessee Technological University Abstract : For a locally compact Abelian group $G$, and a commutative Banach algebra $B$, let $L^1(G,B)$ be the Banach algebra of all Bochner integrable functions. We show that if $G$ is noncompact and $B$ is a semiprime Banach algebras in which every minimal prime ideal is contained in a regular maximal ideal, then $L^1(G,B)$ contains no nontrivial separating ideal. As a consequence we deduce some automatic continuity results for $L^1(G,B)$. Keywords : locally compact abelian groups, Banach algebras, separating ideal MSC numbers : 46J05, 46J20, 43A10, 43A20 Downloads: Full-text PDF