Conjugation‐Invariant Subspaces and Lie Ideals in Non‐Selfadjoint Operator Algebras | Zendy

Marcoux L. W. | Zendy; Sourour A. R. | Zendy

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

Author(s) -

Marcoux L. W.,

Sourour A. R.

Publication year - 2002

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s002461070100299x

Subject(s) - linear subspace , invertible matrix , mathematics , reflexive operator algebra , pure mathematics , invariant (physics) , invariant subspace , nest algebra , lie algebra , subspace topology , multiplicity (mathematics) , algebra over a field , non associative algebra , lie conformal algebra , compact operator , computer science , mathematical analysis , extension (predicate logic) , mathematical physics , programming language

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 −1 Sa=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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