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CONJUGATION-INVARIANT SUBSPACES AND LIE IDEALS IN NON-SELFADJOINT OPERATOR ALGEBRAS

Published online by Cambridge University Press:  24 March 2003

L. W. MARCOUX  and
A. R. SOUROUR
L. W. MARCOUX
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1; [email protected]
A. R. SOUROUR
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4; [email protected]
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Abstract

It is shown that a weakly closed subspace ${\cal S}$ of a nest algebra ${\cal A}$ is closed under conjugation by invertible elements in ${\cal A}$ , that is, $a^{-1}{\cal S}\,a={\cal S}$ if and only if ${\cal S}$ is a Lie ideal. A similar result holds for not-necessarily-closed subspaces of algebras of infinite multiplicity. An explicit characterisation of weakly closed Lie ideals in a nest algebra is given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 493 - 512
Copyright
The London Mathematical Society, 2002

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Footnotes

The authors' research was in part supported by the NSERC of Canada.