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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If is a C*-algebra and is a self-adjoint idempotent, the mapping is called a compression on . 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.

**1.**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**0377549**, 10.1090/S0002-9904-1975-13875-4**2.**M. K. Bennett and D. J. Foulis,*Interval and scale effect algebras*, Adv. in Appl. Math.**19**(1997), no. 2, 200–215. MR**1459498**, 10.1006/aama.1997.0535**3.**David J. Foulis,*Removing the torsion from a unital group*, Rep. Math. Phys.**52**(2003), no. 2, 187–203. MR**2016215**, 10.1016/S0034-4877(03)90012-7**4.**R. J. Greechie, D. Foulis, and S. Pulmannová,*The center of an effect algebra*, Order**12**(1995), no. 1, 91–106. MR**1336539**, 10.1007/BF01108592**5.**K. R. Goodearl,*Partially ordered abelian groups with interpolation*, Mathematical Surveys and Monographs, vol. 20, American Mathematical Society, Providence, RI, 1986. MR**845783****6.**Franklin E. Schroeck Jr.,*Quantum mechanics on phase space*, Fundamental Theories of Physics, vol. 74, Kluwer Academic Publishers Group, Dordrecht, 1996. MR**1374789****7.**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”)*, Translated from the French by Leo F. Boron, Frederick Ungar Publishing Co., New York, 1960. MR**0117561**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
47A20,
06F20,
06F25

Retrieve articles in all journals with MSC (2000): 47A20, 06F20, 06F25

Additional Information

**David J. Foulis**

Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003

Email:
foulis@math.umass.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07644-0

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