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Weighted model spaces and Schmidt subspaces of Hankel operators

Research output: Contribution to journalArticle

Patrick Gérard, Alexander Pushnitski

Original languageEnglish
Pages (from-to)271-298
Number of pages28
JournalJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume101
Issue number1
Early online date5 Aug 2019
DOIs
Publication statusPublished - 25 Feb 2020

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Abstract

For a bounded Hankel matrix (Formula presented.), we describe the structure of the Schmidt subspaces of (Formula presented.), namely the eigenspaces of (Formula presented.) corresponding to non-zero eigenvalues. We prove that these subspaces are in correspondence with weighted model spaces in the Hardy space on the unit circle. Here we use the term ‘weighted model space’ to describe the range of an isometric multiplier acting on a model space. Further, we obtain similar results for Hankel operators acting in the Hardy space on the real line. Finally, we give a streamlined proof of the Adamyan–Arov–Krein theorem using the language of weighted model spaces.

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