Automatic continuity of derivations on algebras
Authors:
Madjid Mirzavaziri and Mohammad Sal Moslehian
Journal:
Proc. Amer. Math. Soc. 134 (2006), 33193327
MSC (2000):
Primary 46L57; Secondary 46L05, 47B47
Published electronically:
June 6, 2006
MathSciNet review:
2231917
Fulltext PDF Free Access
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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 socalled  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:
http://dx.doi.org/10.1090/S0002993906083766
PII:
S 00029939(06)083766
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.
