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Extension of Jauch–Piron states on Jordan algebras

Published online by Cambridge University Press:  24 October 2008

L. J. Bunce  and
J. Hamhalter
L. J. Bunce
Affiliation:
Mathematics Department, Reading University, Reading, RG6 2AX
J. Hamhalter
Affiliation:
Department of Mathematics, Technical University of Prague, Technika 2, 166 27 Prague 6, Czech Republic
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Extract

A state ρ on a JW-algebra or von Neumann algebra M is said to be a Jauch–Piron state if whenever e and f are projections in M with ρ(e) = ρ(f) = 0 then ρ(e ∨ f) = 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 2 , February 1996 , pp. 279 - 286
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Ajupov, S. A.. Extension of traces and type criterions for Jordan algebras of self-adjoint operators. Math. Zeit. 181 (1982), 253–268.CrossRefGoogle Scholar
[2]Amann, A.. Jauch-Piron states in W*-algebras quantum mechanics. J. Math. Phys. 28 (10) (1989), 2384–2389.CrossRefGoogle Scholar
[3]Bunce, L. J. and Hamhalter, J.. Jauch-Piron States on von Neumann algebras. Math. Zeit. 215 (1994), 491–502.CrossRefGoogle Scholar
[4]Chu, C.-H., Dang, T., Russo, B. and Ventura, B.. Surjective isometries of real C*-algebras. J. London Math. Soc. 47 (1993), 97–118.CrossRefGoogle Scholar
[5]Hamhalter, J.. Pure Jauch-Piron States on von Neumann algebras. Ann. Inst. Henri Poincaré. Phys. Théorique 58 (1993), 173–187.Google Scholar
[6]Hance-Olsen, H.. Split faces and ideal structure in operator algebras. Math. Scand. 48 (1981), 137–144.CrossRefGoogle Scholar
[7]Hanche-Olsen, H.. On the structure and tensor products of JC-algebras. Can. J. Math. 35 (1983), 1059–1074.CrossRefGoogle Scholar
[8]Hanche-Olsen, H. and Størmer, E.. Jordan operator algebras (Pitman, 1984).Google Scholar
[9]Jacobson, N.. Structure and representations of Jordan algebras (Amer. Math. Soc. Colloq. Publ. 39 Providence, 1968).Google Scholar
[10]Jauch, J. M.. Foundations of quantum mechanics (Addison-Wesley, 1968).Google Scholar
[11]Jauch, J. M. and Piron, C.. On the structure of quantum proposition systems. Helv. Phys. Acta 42 (1969), 827–837.Google Scholar
[12]Pedersen, G. K.. C*-algebras and their automorphism groups (Academic Press, 1979).Google Scholar
[13]Stacey, P. J.. Local and global splittings in the state space of a JB-algebra. Math. Ann. 256 (1981), 497–507.CrossRefGoogle Scholar
[14]Stacey, P. J.. The structure of Type I JBW-algebras. Math. Proc. Camb. Phil. Soc. 90 (1981), 477–482.Google Scholar
[15]Størmer, E. M.. On antiautomorphisms of von Neumann algebras. Pacific J. Math. 21 (1967), 349–370.CrossRefGoogle Scholar
[16]Stratilla, S. and Zsido, L.. Lectures on von Neumann algebras (Abacus Press, 1979).Google Scholar
[17]Takesaki, M.. Theory of Operator Algebras I (Springer-Verlag, 1979).CrossRefGoogle Scholar