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

 

Compressions on partially ordered abelian groups


Author: David J. Foulis
Journal: Proc. Amer. Math. Soc. 132 (2004), 3581-3587
MSC (2000): Primary 47A20; Secondary 06F20, 06F25
Published electronically: July 22, 2004
MathSciNet review: 2084080
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Abstract: If $A$ is a C*-algebra and $p\in A$ is a self-adjoint idempotent, the mapping $a\mapsto pap$ is called a compression on $A$. We introduce effect-ordered rings as generalizations of unital C*-algebras and characterize compressions on these rings. The resulting characterization leads to a generalization of the notion of compression on partially ordered abelian groups with order units.


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Additional Information

David J. Foulis
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
Email: foulis@math.umass.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07644-0
PII: S 0002-9939(04)07644-0
Keywords: Compression, C*-algebra, projection, partially ordered abelian group, order unit, retraction, unital group, compressible group, effect-ordered ring.
Received by editor(s): June 8, 2003
Published electronically: July 22, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society