Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-02-02T05:00:25.886Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[2]Dunford, N. and Schwartz, J. T., Linear operators,(Interscience, 1958).Google Scholar
[3]Ringrose, J. R., “Automatic continuity of derivations on operator algebras”, J. London Maths. Soc. 5 (1972), 432–438.CrossRefGoogle Scholar