Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space
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- by Stefan Richter and James Sunkes
- Proc. Amer. Math. Soc. 144 (2016), 2575-2586
- DOI: https://doi.org/10.1090/proc/12922
- Published electronically: October 20, 2015
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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 $H^2_d$.References
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Bibliographic Information
- Stefan Richter
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- MR Author ID: 215743
- Email: richter@math.utk.edu
- James Sunkes
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- Email: sunkes@math.utk.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2575-2586
- MSC (2010): Primary 47A15, 47B35; Secondary 47B32
- DOI: https://doi.org/10.1090/proc/12922
- MathSciNet review: 3477074