Reflexive Operator Algebras on Banach Spaces
Functional Analysis
2013-06-11 v2 Operator Algebras
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.
Cite
@article{arxiv.1204.0551,
title = {Reflexive Operator Algebras on Banach Spaces},
author = {Florence Merlevède and Costel Peligrad and Magda Peligrad},
journal= {arXiv preprint arXiv:1204.0551},
year = {2013}
}
Comments
15 pages