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Derivations on commutative operator algebras

Published online by Cambridge University Press:  17 April 2009

Mark Spivack
Mark Spivack
Affiliation:
D. A. M. T. P., The University, Silver Street, Cambridge, England.
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Abstract

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It is well-known that any derivation on a commutative von Neumann algebra is implemented by a bounded operator. In this note we present a simple alternative proof, which generalizes the result further within Hilbert space, and to reflexive Banach spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 415 - 418
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Dixmier, J., Les algébres d'opèrateurs dans l'espace Hilbertien, 2nd edition (Gauthier-Villars, 1969).Google Scholar
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[3]Ringrose, J. R., “Automatic continuity of derivations on operator algebras”, J. London Maths. Soc. 5 (1972), 432–438.CrossRefGoogle Scholar