CONJUGATION-INVARIANT SUBSPACES AND LIE IDEALS IN NON-SELFADJOINT OPERATOR ALGEBRAS
Published online by Cambridge University Press: 24 March 2003
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.
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- Research Article
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- Copyright
- The London Mathematical Society, 2002
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