Compressions on partially ordered abelian groups
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- by David J. Foulis
- Proc. Amer. Math. Soc. 132 (2004), 3581-3587
- DOI: https://doi.org/10.1090/S0002-9939-04-07644-0
- Published electronically: July 22, 2004
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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.References
- Erik M. Alfsen and Frederic W. Shultz, On the geometry of noncommutative spectral theory, Bull. Amer. Math. Soc. 81 (1975), no. 5, 893–895. MR 377549, DOI 10.1090/S0002-9904-1975-13875-4
- M. K. Bennett and D. J. Foulis, Interval and scale effect algebras, Adv. in Appl. Math. 19 (1997), no. 2, 200–215. MR 1459498, DOI 10.1006/aama.1997.0535
- David J. Foulis, Removing the torsion from a unital group, Rep. Math. Phys. 52 (2003), no. 2, 187–203. MR 2016215, DOI 10.1016/S0034-4877(03)90012-7
- R. J. Greechie, D. Foulis, and S. Pulmannová, The center of an effect algebra, Order 12 (1995), no. 1, 91–106. MR 1336539, DOI 10.1007/BF01108592
- K. R. Goodearl, Partially ordered abelian groups with interpolation, Mathematical Surveys and Monographs, vol. 20, American Mathematical Society, Providence, RI, 1986. MR 845783, DOI 10.1090/surv/020
- Franklin E. Schroeck Jr., Quantum mechanics on phase space, Fundamental Theories of Physics, vol. 74, Kluwer Academic Publishers Group, Dordrecht, 1996. MR 1374789, DOI 10.1007/978-94-017-2830-0
- Béla Sz.-Nagy, Extensions of linear transformations in Hilbert space which extend beyond this space (Appendix to Frigyes Riesz and Béla Sz.-Nagy, “Functional analysis”), Frederick Ungar Publishing Co., New York, 1960. Translated from the French by Leo F. Boron. MR 0117561
Bibliographic Information
- David J. Foulis
- Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
- Email: foulis@math.umass.edu
- Received by editor(s): June 8, 2003
- Published electronically: July 22, 2004
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3581-3587
- MSC (2000): Primary 47A20; Secondary 06F20, 06F25
- DOI: https://doi.org/10.1090/S0002-9939-04-07644-0
- MathSciNet review: 2084080