Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T13:44:55.443Z Has data issue: false hasContentIssue false
  • English
  • Français

Essentially defined derivations on semisimple Banach algebras

Published online by Cambridge University Press:  20 January 2009

A. R. Villena
A. R. Villena
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain, E-mail address: [email protected]
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.

We prove that every partially defined derivation on a semisimple complex Banach algebra whose domain is a (non necessarily closed) essential ideal is closable. In particular, we show that every derivation defined on any nonzero ideal of a prime C*-algebra is continuous.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 175 - 179
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1. Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073.Google Scholar
2. Mathieu, M., Elementary operators on prime C*-algebras. I. Math. Ann. 284 (1989), 223–244.Google Scholar
3. Rodriguez, A., Jordan structures in Analysis, in Jordan algebras: Proceedings of a Conference held at Oberwolfach, August 9–15, 1992 (Edited by Kaup, W., McCrimmon, K. and Peterson, H.. Walter de Gruyter, Berlin-New York 1994), 97–186.Google Scholar