For a Hankel operator , , on the Hardy space over the bidisk, is an invariant subspace of . It is known that there is an invariant subspace such that for every . Let be a nonconstant function. It is proved that if for Blaschke products and , then for some subproducts and of and , respectively. If is -cyclic, then it is easy to see that . We give some examples satisfying but is not -cyclic.
"Kernels of Hankel operators on the Hardy space over the bidisk." Banach J. Math. Anal. 13 (3) 612 - 626, July 2019. https://doi.org/10.1215/17358787-2019-0020