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arXiv · 1511.02981

Absolute continuity for commuting row contractions

Raphaël Clouâtre·Kenneth R. Davidson
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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.

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BibTeXRIS

Raphaël Clouâtre, Kenneth R. Davidson. 2016-05-09. Absolute continuity for commuting row contractions. https://arxiv.org/abs/1511.02981

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