Automatic continuity of -derivations on -algebras

Authors:
Madjid Mirzavaziri and Mohammad Sal Moslehian

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3319-3327

MSC (2000):
Primary 46L57; Secondary 46L05, 47B47

DOI:
https://doi.org/10.1090/S0002-9939-06-08376-6

Published electronically:
June 6, 2006

MathSciNet review:
2231917

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.

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Additional Information

**Madjid Mirzavaziri**

Affiliation:
Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran

Email:
mirzavaziri@math.um.ac.ir

**Mohammad Sal Moslehian**

Affiliation:
Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran

Email:
moslehian@ferdowsi.um.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-06-08376-6

Keywords:
$*$-$(\sigma,\tau)$-derivation,
$\sigma$-derivation,
derivation,
automatic continuity,
$C^*$-algebra

Received by editor(s):
May 26, 2005

Received by editor(s) in revised form:
June 1, 2005

Published electronically:
June 6, 2006

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.