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Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space


Authors: Stefan Richter and James Sunkes
Journal: Proc. Amer. Math. Soc. 144 (2016), 2575-2586
MSC (2010): Primary 47A15, 47B35; Secondary 47B32
DOI: https://doi.org/10.1090/proc/12922
Published electronically: October 20, 2015
MathSciNet review: 3477074
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Abstract: We show that every nonzero invariant subspace of the Drury-Arveson space $ H^2_d$ of the unit ball of $ \mathbb{C}^d$ is an intersection of kernels of little Hankel operators. We use this result to show that if $ f$ and $ 1/f\in H^2_d$, then $ f$ is cyclic in $ H^2_d$.


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Additional Information

Stefan Richter
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: richter@math.utk.edu

James Sunkes
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: sunkes@math.utk.edu

DOI: https://doi.org/10.1090/proc/12922
Received by editor(s): May 25, 2015
Received by editor(s) in revised form: July 18, 2015
Published electronically: October 20, 2015
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2015 American Mathematical Society