Continuity of derivations, intertwining maps, and cocycles from Banach algebras

Dales, H.G. and Villena, A. R. (2001) Continuity of derivations, intertwining maps, and cocycles from Banach algebras. Journal of the London Mathematical Society, 63 (1). pp. 215-225. ISSN 0024-6107

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Abstract

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S:A→E is intertwining if the bilinear map Formula is continuous, and a linear map D:A→E is a derivation if δ1D=0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continuity of all intertwining maps from a Banach algebra A into each Banach A-bimodule follows from the fact that all derivations from A into each such bimodule are continuous; this resolves a question left open in [1, p. 36]. Indeed, we prove a somewhat stronger result involving left- (or right-) intertwining maps.

Item Type: Journal Article
Journal or Publication Title: Journal of the London Mathematical Society
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 67589
Deposited By: ep_importer_pure
Deposited On: 19 Nov 2013 10:59
Refereed?: Yes
Published?: Published
Last Modified: 30 Sep 2019 17:46
URI: https://eprints.lancs.ac.uk/id/eprint/67589

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