Confluent operator algebras and the closability property
Abstract
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.
Cite
@article{arxiv.0908.0729,
title = {Confluent operator algebras and the closability property},
author = {H. Bercovici and R. G. Douglas and C. Foias and C. Pearcy},
journal= {arXiv preprint arXiv:0908.0729},
year = {2009}
}
Comments
Preliminary version