Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators

By Anton Baranov, I. Chalendar, Emmanuel Fricain, Javad Mashreghi, Dan Timotin. 2009

85 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/34f7e01c88317e9aa6f1600c98bbef925a2d0dcf

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Recent Progress on Truncated Toeplitz Operators (2011, background): “ Corollary 8. If uis a one-component inner function, then every operator in Tu has a bounded symbol. 26 Stephan Ramon Garcia and William T. Ross Of course the natural question now (and conjectured in [14]) is the following: Question 2 Is the converse of the preceding corollary true? It turns out tha”
Symbols of truncated Toeplitz operators (2010, background): “This statement was conjectured in [9].”
Algebras of truncated Toeplitz operators (2010, background): “The case of |α| = 1 is indirectly dealt with in [11, 1] and we collect those results here.”
Asymmetric truncated Toeplitz operators and Toeplitz operators with matrix symbol (2015, background): “where I = I1 = [0, λ], has been highlighted, for instance, in [1].”