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Article Dans Une Revue Journal of Functional Analysis Année : 2010

Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators.

Résumé

Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ 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.
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Dates et versions

hal-00412228 , version 1 (01-09-2009)
hal-00412228 , version 2 (14-11-2009)

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A. Baranov, Isabelle Chalendar, Emmanuel Fricain, Javad Mashreghi, Dan Timotin. Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators.. Journal of Functional Analysis, 2010, 259 (10), pp.2673-2701. ⟨hal-00412228v2⟩
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