A Note on Derivations of Pro-C*-Algebras into Complete Locally Convex Bimodules

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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 143-152


M. Weigt

Department of Mathematics and Applied Mathematics

Nelson Mandela Metropolitan University

Summerstrand Campus (South)

Port Elizabeth 6031, South Africa

mailto:Martin.Weigt@nmmu.ac.za

I. Zarakas

Department of Mathematics,

University of Athens,

Panepistimiopolis,

Athens 15784, Greece

mailto:gzarak@math.uoa.gr




Abstract A result of J. R. Ringrose says that, given a C * -algebra A and a Banach A-bimodule X, every derivation \delta : A \rightarrow X is continuous. In this note, we give some extensions of this result to the case where A is a pro-C * -algebra and X a complete locally convex A-bimodule.

Keywords Pro-C*-algebra, locally convex bimodule, Banach A-bimodule, derivation.

Classification (MSC2000) 46H05, 46H25, 46H40, 46K05.

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