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Lie and Jordan structure in operator algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Derek W. Robinson  and
Erling Størmer
Derek W. Robinson
Affiliation:
Department of Pure Mathematics University of New South WalesPO Box, 1, Kensington 2033, Australia
Erling Størmer
Affiliation:
Institute of Mathematics University of OsloPO Box 1053, Blindern, Oslo 3, Norway
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Abstract

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Let υ be a C*-algebra, α a *-anti-automorphism of order 2, and υα(±1) = {A; A ∈ υ, α(A) = ± A} the spectral subspaces of α. It follows that υα(+ 1) is a Jordan algebra and υα(− 1) is a Lie algebra. We begin the classification of pairs of Jordan and Lie algebras which can occur in this manner by examining υ = ℒ(ℋ), the algebra of bounded operators on a Hilbert space ℋ.

MSC classification

Secondary: 46L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 2 , March 1980 , pp. 129 - 142
Copyright
Copyright © Australian Mathematical Society 1980

References

Arazy, J. and Friedman, Y. (1978), ‘Contractive projections in C1 and C∞’, Mem. Amer. Math. Soc. 200.Google Scholar
Effros, E. and Størmer, E. (1979) ‘Positive projections and Jordan structure in operator algebras’, Math. Scand., to appear.Google Scholar
Jordan, P., von Neumann, J. and Wigner, E. (1934), ‘On an algebraic generalization of the quantum mechanical formalism’, Ann. of Math. 35, 29–64.CrossRefGoogle Scholar
Størmer, E. (1966), ‘Jordan algebras of type 1’, Acta Math. 115, 165–184.CrossRefGoogle Scholar
Størmer, E. (1968), ‘Irreducible Jordan algebras of self-adjoint operators’, Trans. Amer. Math. Soc. 130, 153–166.CrossRefGoogle Scholar
Størmer, E. (1972), ‘On projection maps of von Neumann algebras’, Math. Scand. 30, 46–50.CrossRefGoogle Scholar
Størmer, E. (1979), ‘Decomposition of positive projections on C*-algebras’, preprint.Google Scholar
Tomiyama, J. (1959), ‘On the projection of norm one in W*-algebras. III’, Tôhoku Math. J. 11, 125–129.Google Scholar
Wan, Z-X (1975), Lie algebras (Pergamon Press, Oxford).Google Scholar