Continuity of epimorphisms and derivations on vector-valued group algebras |
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Authors: | Michael M. Neumann M. Victoria Velasco |
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Affiliation: | (1) Department of Mathematics & Statistics, Mississippi State University, 39762 Mississippi State, MS, USA;(2) Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | 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. Dedicated to Heinz Konig on the occasion of his 65th birthday Research supported by Grant SNF 11-1015 from the Danish Science Research Council. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (1991) 46H40 43A22 |
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