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Semifinite traces on JBW-algebras

Published online by Cambridge University Press:  24 October 2008

W. P. C. King
W. P. C. King
Affiliation:
Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham, Swindon, Wilts SN6 8LA
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Extract

A JB-algebra is a real Jordan algebra A which is also a Banach space and whose norm and multiplication satisfy the two following conditions

(i) ∥a2∥ = ∥a∥2,

(ii) ∥a2 − b2∥ ≤ max{∥a2∥, ∥b2∥},

for all elements a and b in A. A JB-algebra which is also a Banach dual space is called a JBW-algebra. The properties of JB-algebras and JBW-algebras can be found in (3), (4), (8) and (15).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 503 - 509
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Alfsen, E. M. Compact convex sets and boundary integrals. Ergebnisse der Math. vol. 57 (Springer-Verlag, 1971).Google Scholar
(2)Alfsen, E. M. and Shultz, F. W.Non commutative spectral theory for affine-function spaces on convex sets. Mem. Amer. Math. Soc. 172 (1976).Google Scholar
(3)Alfsen, E. M. and Shultz, F. W.State spaces of Jordan algebras. Acta Math. 140 (1978), 155–190.CrossRefGoogle Scholar
(4)Alfsen, E. M., Shultz, F. W. and Stormer, E.A Gelfand-Naimark theorem for Jordan algebras. Advances in Math. 28 (1978), 11–27.CrossRefGoogle Scholar
(5)Bellissard, J. and Iochum, B.Homogeneous self dual cones versus Jordan algebras: the theory revisited. Ann. Inst. Fourier, Grenoble 28, 1 (1978), 27–67.CrossRefGoogle Scholar
(6)Dunford, M. and Schwartz, J. T.Linear operators, vol. 1 (Interscience, New York, 1957).Google Scholar
(7)Edwards, C. M.Ideal theory in JB-algebras. J. Land. Math. Soc. (2), 16 (1977), 507–513.CrossRefGoogle Scholar
(8)Edwards, C. M.On the centres of hereditary JBW-algebras of a JBW-algebra. Math. Proc. Camb. Philos. Soc. 85 (1979), 317–324.CrossRefGoogle Scholar
(9)Edwards, C. M.On the facial structure of a JB-algebra. J. Land. Math. Soc. (2), 19 (1979), 335–344.Google Scholar
(10)Edwards, C. M.Multipliers of JB-algebras. Math. Ann. 249 (1980), 265–272.CrossRefGoogle Scholar
(11)Emch, G. G. and King, W. P. C. Faithful normal states on JBW-algebras;(Preprint.)Google Scholar
(12)Murray, F. J. and Von Neumann, J.On rings of operators. II. Trans. Amer. Math. Soc. 41 (1937), 208–248.CrossRefGoogle Scholar
(13)Pedersen, G. K. C*-algebras and their automorphism groups. Lond. Math. Soc. Monographs no. 14 (Academic Press, London, 1979).Google Scholar
(14)Pedersen, G. K. and Stormer, E. Traces on JB-algebras. (Preprint.)Google Scholar
(15)Shultz, F. W.On normed Jordan algebras which are Banach dual spaces. J. Funct. Anal. 31 (1979), 360–376.Google Scholar