Schmidt subspaces of block Hankel operators

Abstract

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.

19 Pages, Revised Version, To appear in J. Operator Theory