Schmidt subspaces of block Hankel operators

In scalar-valued Hardy space, the class of Schmidt subspaces for a bounded Hankel operator are closely related to nearly $S^{\ast }$-invariant subspaces, as described by Gérard and Pushnitski. In this article, we prove that these subspaces in the context of vector-valued Hardy spaces are nearly $S^{\ast }$-invariant with finite defect in general. As a consequence, we obtain a short proof of the characterization results concerning the Schmidt subspaces in scalar-valued Hardy space in an alternative way. Thus, our work complements the work of Gérard and Pushnitski regarding the structure of Schmidt subspaces.