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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.

Keywords: Toeplitz quadratic forms, closed operators and quadratic forms, absolutely continuous measures

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