A Dixmier-Schaefer-Zhang theorem for operator algebras
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- by L. J. Bunce, Kazuyuki Saitô and J. D. Maitland Wright PDF
- Proc. Amer. Math. Soc. 127 (1999), 2975-2979 Request permission
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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2975-2979
- MSC (1991): Primary 46L05, 28A60
- DOI: https://doi.org/10.1090/S0002-9939-99-04904-7
- MathSciNet review: 1610924