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

Richter, Stefan; Sunkes, James

doi:10.1090/proc/12922

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 $H^2_d$.

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