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Journal of Operator Theory

Volume 83, Issue 2, Spring 2020  pp. 321-331.

A Beurling theorem for almost-invariant subspaces of the shift operator

Authors:  Isabelle Chalendar (1), Eva A. Gallardo-Guti\'errez (2), Jonathan R. Partington (3)
Author institution:(1) Universit\'e Paris-Est, LAMA, (UMR 8050), UPEM, UPEC, CNRS, F-77454, Marne-la-Vall\'ee, France
(2) Universidad Complutense de Madrid and ICMAT, Departamento de An\'alisis Matem\'atico y Matem\'atica Aplicada, Fa\-cul\-tad de Ciencias Matem\'aticas, Plaza de Ciencias 3, 28040, Madrid, Spain
(3)School of Mathematics, Univ. of Leeds, Leeds LS2 9JT, U.K.

Summary: A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorems. As a corollary we describe the almost-invariant subspaces for the shift and its adjoint.

Keywords: Beurling theorem, nearly-invariant subspaces, almost-invariant subspaces

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