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arXiv · 1204.0551

Reflexive Operator Algebras on Banach Spaces

Florence Merlevède·Costel Peligrad·Magda Peligrad
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Abstract

In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of finite uniform multiplicity and with the direct sum property, then it is reflexive, i.e. it contains every operator that leaves invariant every closed subspace in the invariant subspace lattice of the algebra. In particular, such algebras coincide with their bicommutant.

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Florence Merlevède, Costel Peligrad, Magda Peligrad. 2012-04-02. Reflexive Operator Algebras on Banach Spaces. https://arxiv.org/abs/1204.0551

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