Journal of Operator Theory
Volume 77, Issue 1, Winter 2017 pp. 205-216.
On semibounded Toeplitz operators
Authors:
D.R. Yafaev
Author institution:IRMAR, Universite de Rennes I, Campus de
Beaulieu, 35042 Rennes Cedex, France
Summary: We show that a semibounded Toeplitz quadratic form is closable in the space $\ell^2({\mathbb Z}_{+})$ if and only if
its entries are Fourier coefficients of an absolutely continuous measure. We also describe the domain of the corresponding closed form. This allows us to define semibounded Toeplitz operators under minimal assumptions on their matrix elements.
DOI: http://dx.doi.org/10.7900/jot.2016mar20.2095
Keywords: Toeplitz quadratic forms, closed operators and quadratic forms, absolutely continuous measures
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