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arXiv · 2301.13080

Schmidt subspaces of block Hankel operators

Arup Chattopadhyay·Soma Das·Chandan Pradhan
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Abstract

In scalar-valued Hardy space, the class of Schmidt subspaces for a bounded Hankel operator are closely related to nearly $S^*$-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 $S^*$-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.

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Arup Chattopadhyay, Soma Das, Chandan Pradhan. 2023-12-28. Schmidt subspaces of block Hankel operators. https://arxiv.org/abs/2301.13080

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