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Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators |
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| Authors: | Anton Baranov Javad Mashreghi |
| Affiliation: | a Department of Mathematics and Mechanics, St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia b Université de Lyon; Université Lyon 1; INSA de Lyon; Ecole Centrale de Lyon; CNRS, UMR5208, Institut Camille Jordan; 43 bld. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France c Département de Mathématiques et de Statistique, Université Laval, Québec, QC, Canada G1K 7P4 d Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 014700, Romania |
| Abstract: | Compressions of Toeplitz operators to coinvariant subspaces of H2 are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol; the second is the Reproducing Kernel Thesis. We show that in general the answer to the first question is negative, and we exhibit some classes of spaces for which the answers to both questions are positive. |
| Keywords: | Toeplitz operators Reproducing Kernel Thesis Model spaces |
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