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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Dixmier-Schaefer-Zhang theorem
for operator algebras


Authors: L. J. Bunce, Kazuyuki Saitô and J. D. Maitland Wright
Journal: Proc. Amer. Math. Soc. 127 (1999), 2975-2979
MSC (1991): Primary 46L05, 28A60
Published electronically: April 28, 1999
MathSciNet review: 1610924
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Abstract: Schaefer and Zhang have recently obtained an analogue, for sequentially order continuous functionals on $C(K)$, of a much earlier theorem of Dixmier. In this note it is shown that the Schaefer-Zhang Theorem has a natural generalisation to non-commutative $C^*$-algebras. These results are obtained as consequences of our main theorem which is concerned with affine functions on compact convex sets.


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Additional Information

Kazuyuki Saitô
Affiliation: Mathematical Institute, Tohoku University, Sendai 980, Japan
Email: saito@math.tohoku.ac.jp

J. D. Maitland Wright
Affiliation: Analysis and Combinatorics Research Centre, Mathematics Department, University of Reading, Reading RG6 6AX, England
Email: j.d.m.wright@rdg.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04904-7
PII: S 0002-9939(99)04904-7
Received by editor(s): August 1, 1997
Received by editor(s) in revised form: January 6, 1998
Published electronically: April 28, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society