Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 309-321.

The Nehari problem for the Hardy space on the torus

Authors: Sarah H. Ferguson
Author institution: Department of Mathematics, Purdue University, Lafayette, IN 47907--1395, U.S.A.

Summary: We explicitly construct functions in ${\bihardy}^{\perp}$ which determine bounded (big) Hankel operators on $\bihardy$ but are not of the form $P_{\perp}{\psi} $ for any $\psi \in \bilinfty $. We use this construction to show that the norm of a Hankel operator with bounded symbol is not, in general, comparable to the distance the symbol is from $\bihinfty$. We also characterize the vector space quotient of symbols of bounded Hankel operators modulo those which lift to $\bilinfty$ in terms of a Toeplitz completion problem on vector-valued Hardy space in one-variable.

Keywords: Hankel operator, Toeplitz operator, Nehari theorem, restricted BMO

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