Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space
Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space
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 $H^2_d$.