Journal article
On continuity of derivations and epimorphisms on some vector-valued group algebras
Bulletin of the Australian Mathematical Society, v 56(2), pp 209-215
01 Oct 1997
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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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Details
- Title
- On continuity of derivations and epimorphisms on some vector-valued group algebras
- Creators
- Ramesh V. Garimella - Tennessee Technological University
- Publication Details
- Bulletin of the Australian Mathematical Society, v 56(2), pp 209-215
- Publisher
- Cambridge University Press
- Number of pages
- 7
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1997YB00800004
- Scopus ID
- 2-s2.0-0031256616
- Other Identifier
- 991021861622904721
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- Web of Science research areas
- Mathematics