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The structure of Schmidt subspaces of Hankel operators: a short proof

Volume 256 / 2021

Patrick Gérard, Alexander Pushnitski Studia Mathematica 256 (2021), 61-71 MSC: 47B35, 30H10. DOI: 10.4064/sm190717-7-2 Published online: 27 May 2020


We give a short proof of the main result of a previous paper of ours: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant subspaces, and our proof uses Hitt’s theorem on the structure of such subspaces. We also give a formula for the action of a Hankel operator on its Schmidt subspace.


  • Patrick GérardUniversité Paris-Saclay, CNRS
    Laboratoire de Mathématiques d’Orsay
    91405 Orsay, France
  • Alexander PushnitskiDepartment of Mathematics
    King’s College London
    Strand, London, WC2R 2LS, U.K.

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