Schmidt Subspaces of Hankel Operators

We consider bounded Hankel operators \(H_{\psi }\) $H_{\psi }$ acting on the Hardy space \(H^2\) $H^2$ to \(L^2\ominus H^2\) $L^2\ominus H^2$ and obtain results on the Schmidt subspaces \(E^+_s(H_\psi )\) $E_s^{+}(H_{\psi })$ of such operators defined as the kernels of \( H_{\psi }^{*}H_{\psi }-s^2I\) $H_{\psi }^{\ast }{H}_{\psi }-s^{2}I$ where \(s>0\) $s>0$ . These spaces have been recently studied in Gérard and Pushnitski (J Lond Math Soc 2(101):271–298, 2020, Studia Math 256:61–71, 2021) in the context of anti-linear Hankel operators. In particular, we prove that for \(s=\Vert H_{\psi }\Vert \) $s=\Vert H_{\psi }\Vert$ the nontrivial Schmidt subspace \(E^+_s(H_\psi )\) $E_s^{+}(H_{\psi })$ is the kernel of a Toeplitz operator.