Journal of Operator Theory

Volume 93, Issue 1, Winter 2025 pp. 229-249.

Schmidt subspaces of block Hankel operators

Authors: Arup Chattopadhyay (1), Soma Das (2), Chandan Pradhan (3)
Author institution: (1) Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India
(2) Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Centre, Bengaluru, 560059, India
(3) Department of Mathematics, Indian Institute of Science Bangalore, Bengaluru, 560012, India

Summary: 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 Gerard 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 Gerard and Pushnitski regarding the structure of Schmidt subspaces.

DOI: http://dx.doi.org/10.7900/jot.2023apr15.243
Keywords: Hankel operators, Schmidt subspace, Hardy space, nearly invariant subspace, model space

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