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On extension of Beurling–Helson–Lowdenslager theorem

On extension of Beurling–Helson–Lowdenslager theorem In this paper, we prove an extension of the Helson–Lowdenslager theorem for L2(T)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {L}^2(\mathbb {T})$$\end{document} for sub - Hilbert spaces under certain axioms. Furthermore, we provide an alternate proof of characterization of shift invariant sub-Hilbert spaces contained in H2(D)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {H}^2(\mathbb {D})$$\end{document} satisfying similar axioms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Operator Theory Springer Journals

On extension of Beurling–Helson–Lowdenslager theorem

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Publisher
Springer Journals
Copyright
Copyright © Tusi Mathematical Research Group (TMRG) 2021
ISSN
2662-2009
eISSN
2538-225X
DOI
10.1007/s43036-021-00158-x
Publisher site
See Article on Publisher Site

Abstract

In this paper, we prove an extension of the Helson–Lowdenslager theorem for L2(T)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {L}^2(\mathbb {T})$$\end{document} for sub - Hilbert spaces under certain axioms. Furthermore, we provide an alternate proof of characterization of shift invariant sub-Hilbert spaces contained in H2(D)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {H}^2(\mathbb {D})$$\end{document} satisfying similar axioms.

Journal

Advances in Operator TheorySpringer Journals

Published: Jul 29, 2021

Keywords: Invariant subspaces; Berezin symbol; 47A15; 47B32; 46E22

References