Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T12:09:26.674Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of Atomic Facially Symmetric Spaces

Published online by Cambridge University Press:  20 November 2018

Yaakov Friedman  and
Bernard Russo
Yaakov Friedman
Affiliation:
Department of Mathematics, Jerusalem College of Technology, P.O. Box 16031, Jerusalem 91 160, Israel
Bernard Russo
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Banach space satisfying some physically significant geometric properties is shown to be the predual of a JBW*–triple. If one considers the unit ball of this Banach space as the state space of a physical system, the result shows that the set of observables is equipped with a natural ternary algebraic structure. This provides a spectral theory and other tools for studying the quantum mechanical measuring process

Keywords

461752
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 33 - 87
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Araki, H., On a characterization of the state space of quantum mechanics, Commun. Math. Phys. 75(1980), 1–24.Google Scholar
2. Arazy, J. and Friedman, Y., Contractive Projections in Cp, C.R.Acad. Sci. Paris 312(1991), 439–444.Google Scholar
3. Arazy, J. and Friedman, Y., Contractive Projections in Cp, Mem. Amer. Math. Soc 459(1992).Google Scholar
4. Alfsen, E. and Shultz, F., State spaces of Jordan algebras, Acta Math. 140(1978), 155–190.Google Scholar
5. Bourgin, R.D., Geometric Aspects of Convex Sets with the Radon-Nikodym Property, Lecture Notes in Math. 993, Springer-Verlag, New York, 1983.Google Scholar
6. Barton, T.J. and Godefroy, G., Remarks on the predual of a JBW*-triple, J. London Math. Soc. (2) 34(1986), 300–304.Google Scholar
7. Chu, Cho-Ho and Iochum, B., On the Radon-Nikodym property in Jordan triples, Proc. A.M.S. 99(1987), 462–464.Google Scholar
8. Dang, T. and Friedman, Y., Classification of ‘JBW* -triple factors and applications , Math. Scand. 61(1987), 292–330.Google Scholar
9. Dineen, S., Klimek, M. and Timoney, R.M., Biholomorphic mappings and Banach function modules, J. reine angew. Math. 387(1988), 122–147.Google Scholar
10. Edwards, C.M. and Ruttiman, G.T., On the facial structure of the unit balls in a JBW*-triple and its predual, J. London Math. Soc. (2) 38(1988), 317–332.Google Scholar
11. Friedman, Y. and Russo, B., Structure of the predual of a JBW* -triple , J. Reine Angew. Math. 356(1985), 67–89.Google Scholar
12. Friedman, Y. and Russo, B., A geometric spectral theorem, Quart. J. Math. Oxford (2) 37(1986), 263–277.Google Scholar
13. Friedman, Y. and Russo, B., Conditional expectation and bicontractiveprojections on Jordan C* -algebras and their generalizations, Math. Zeit. 194(1987), 227–236.Google Scholar
14. Friedman, Y. and Russo, B., Some affine geometric aspects of operator algebras, Pac. J. Math. 137(1989), 123–144.Google Scholar
15. Friedman, Y. and Russo, B., Affine structure of facially symmetric spaces, Math. Proc. Camb. Philos. Soc. 106(1989), 107— 124.Google Scholar
16. Friedman, Y. and Russo, B., Geometry of the Dual Ball of the Spin Factor, Proc. Lon. Math. Soc. (3) 65(1992), 142–174.Google Scholar
17. Hanche-Olsen, H. and Störmer, E., Jordan operator algebras, Pittman, London, 1984.Google Scholar
18. Iochum, B. and Shultz, F., Normal state spaces of Jordan and von Neumann algebras, J. Funct. Anal. 50(1983), 317–328.Google Scholar
19. McCrimmon, K., Compatible Peirce decompositions of Jordan triple systems, Pac. J. Math. 103(1982), 57-102.Google Scholar
20. Neher, E., Jordan Triple Systems by the Grid Approach, Lecture Notes in Math. 1280, Springer-Verlag, New York, 1987.Google Scholar