Absolute continuity for commuting row contractions
Functional Analysis
2016-05-11 v2 Operator Algebras
Abstract
Absolutely continuous commuting row contractions admit a weak- continuous functional calculus. Building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the Drury-Arveson space, we give a complete characterization of these commuting row contractions in measure theoretic terms. We also establish that completely non-unitary row contractions are necessarily absolutely continuous, in direct parallel with the case of a single contraction. Finally, we consider refinements of this question for row contractions that are annihilated by a given ideal.
Cite
@article{arxiv.1511.02981,
title = {Absolute continuity for commuting row contractions},
author = {Raphaël Clouâtre and Kenneth R. Davidson},
journal= {arXiv preprint arXiv:1511.02981},
year = {2016}
}
Comments
20 pages. Small issues in the proof of Theorem 4.2 have been fixed. Final version. To appear in Journal of Functional Analysis