Continuity of Derivations, Intertwining Maps, and Cocycles from Banach Algebras |
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Authors: | Dales H G; Villena A R |
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Institution: | Department of Pure Mathematics, University of Leeds Leeds LS2 9JT
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada Granada, Spain |
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Abstract: | Let A be a Banach algebra, and let E be a Banach A-bimodule.A linear map S:AE is intertwining if the bilinear map
is continuous, and a linear map D:AE is a derivation if 1D=0,so that a derivation is an intertwining map. Derivations fromA to E are not necessarily continuous. The purpose of the present paper is to prove that the continuityof all intertwining maps from a Banach algebra A into each BanachA-bimodule follows from the fact that all derivations from Ainto each such bimodule are continuous; this resolves a questionleft open in 1, p. 36]. Indeed, we prove a somewhat strongerresult involving left- (or right-) intertwining maps. |
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