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
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