Continuity of epimorphisms and derivations on vector-valued group algebras

This paper deals with the automatic continuity theory for the convolution algebra of all Bochner integrable functions from a locally compact abelian group G into an arbitrary unital complex Banach algebra A. For non-compact G, it is shown that all epimorphisms and all derivations on this vector-valu...

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Bibliographic Details
Published in:Archiv der Mathematik 1997-02, Vol.68 (2), p.151-158
Main Authors: Neumann, Michael M., Velasco, M. Victoria
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
Group theory
Mathematical analysis
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Summary:This paper deals with the automatic continuity theory for the convolution algebra of all Bochner integrable functions from a locally compact abelian group G into an arbitrary unital complex Banach algebra A. For non-compact G, it is shown that all epimorphisms and all derivations on this vector-valued group algebra are necessarily continuous while for compact G, such results depend heavily on the automatic continuity properties of the range algebra a.
ISSN:0003-889X
1420-8938
DOI:10.1007/s000130050044