CONTINUITY OF EPIMORPHISMS AND DERIVATIONS ON VECTOR-VALUED GROUP-ALGEBRAS

Authors
NEUMANN MM VELASCO MV
Citation
Mm. Neumann et Mv. Velasco, CONTINUITY OF EPIMORPHISMS AND DERIVATIONS ON VECTOR-VALUED GROUP-ALGEBRAS, Archiv der Mathematik, 68(2), 1997, pp. 151-158
Citations number
16
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Archiv der Mathematik → ACNP
ISSN journal
0003889X
Volume
68
Issue
2
Year of publication
1997
Pages
151 - 158
Database
ISI
SICI code
0003-889X(1997)68:2<151:COEADO>2.0.ZU;2-I
Abstract
This paper deals with the automatic continuity theory for the convolut ion algebra of all Bochner integrable functions from a locally compact abelian group G into an arbitrary unital complex Banach algebra A. Fo r 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.