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On continuity of derivations and epimorphisms on some vector-valued group algebras
Journal article   Open access   Peer reviewed

On continuity of derivations and epimorphisms on some vector-valued group algebras

Ramesh V. Garimella
Bulletin of the Australian Mathematical Society, v 56(2), pp 209-215
01 Oct 1997
url
https://doi.org/10.1017/S0004972700030938View
Published, Version of Record (VoR) Open

Abstract

For a locally compact Abelian group G and a commutative Banach algebra B, let L1(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is compact and B is a nonunital Banach algebra without nontrivial zero divisors, then (i) all derivations on L1(G, B) are continuous if and only if all derivations on B are continuous, and (ii) each epimorphism from a Banach algebra X onto L1(G, B) is continuous provided every epimorphism from X onto B is continuous. If G is noncompact then every derivation on L1(G, B) and every epimorphism from a commutative Banach algebra onto L1(G, B) are continuous. Our results extend the results of Neumann and Velasco for nonunital Banach algebras.

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