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New York Journal of Mathematics
Volume 27 (2021), 1597-1612

  

Chafiq Benhida, Emmanuel Fricain, and Dan Timotin

Reducing subspaces of C00 contractions

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Published: December 8, 2021.
Keywords: Truncated Toeplitz operators, reducibility, model space.
Subject: 47B35,47A15,47B38.

Abstract
Using the Sz.-Nagy--Foias theory of contractions, we obtain general results about reducibility for a class of completely nonunitary contractions. These are applied to certain truncated Toeplitz operators, previously considered by Li--Yang--Lu and Gu. In particular, a negative answer is given to a conjecture stated by the latter.

Acknowledgements

This work was partially supported by Labex CEMPI (ANR-11-LABX-0007).


Author information

Chafiq Benhida:
Laboratoire Paul Painlevé
Université Lille 1
59 655 Villeneuve d'Ascq Cédex, France

chafiq.benhida@univ-lille.fr

Emmanuel Fricain:
Laboratoire Paul Painlevé
Université Lille 1
59 655 Villeneuve d'Ascq Cédex, France

emmanuel.fricain@univ-lille.fr

Dan Timotin:
Simion Stoilow Institute of Mathematics
The Romanian Academy
PO Box 1-764, Bucharest 014700, Romania

Dan.Timotin@imar.ro