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Journal of the London Mathematical Society 2002 65(2):493-512; doi:10.1112/S002461070100299X
© 2002 by London Mathematical Society
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© The London Mathematical Society

Conjugation-Invariant Subspaces and Lie Ideals in Non-Selfadjoint Operator Algebras

L. W. Marcoux and A. R. Sourour

Department of Mathematics, University of Alberta Edmonton, Alberta, Canada T6G 2G1, l.marcoux{at}ualberta.ca
Department of Mathematics and Statistics, University of Victoria Victoria, BC, Canada V8W 3P4, sourour{at}math.uvic.ca

Received 11 October 2000. Revision received 24 July 2001.

It is shown that a weakly closed subspace S of a nest algebra A is closed under conjugation by invertible elements in A, that is, a–1Sa=S if and only if 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.


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