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A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor


Authors: Raphaël Clouâtre, Michael Hartz and Dominik Schillo
Journal: Proc. Amer. Math. Soc. 148 (2020), 731-740
MSC (2010): Primary 47A15; Secondary 47B32, 46E22
DOI: https://doi.org/10.1090/proc/14736
Published electronically: August 7, 2019
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Abstract: We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record factorization results for pairs of nested invariant subspaces.


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Additional Information

Raphaël Clouâtre
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email: raphael.clouatre@umanitoba.ca

Michael Hartz
Affiliation: Fakultät für Mathematik und Informatik, FernUniversität in Hagen, 58084 Hagen, Germany
Email: michael.hartz@fernuni-hagen.de

Dominik Schillo
Affiliation: Fachrichtung Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbücken, Germany
Email: schillo@math.uni-sb.de

DOI: https://doi.org/10.1090/proc/14736
Keywords: Invariant subspaces, Beurling's theorem, Nevanlinna--Pick kernels
Received by editor(s): May 14, 2019
Received by editor(s) in revised form: June 2, 2019
Published electronically: August 7, 2019
Additional Notes: The first author was partially supported by an NSERC Discovery grant.
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2019 American Mathematical Society