# 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

I. Zarakas

Department of Mathematics,

University of Athens,

Panepistimiopolis,

Athens 15784, Greece

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.