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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

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