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

### From NZJM

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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

**Abstract** A result of J. R. Ringrose says that, given a *C*^{ * }-algebra A and a Banach *A*-bimodule *X*, every
derivation 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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