Journal of Operator Theory
Volume 53, Issue 2, Spring 2005 pp. 431-440.
Compact Toeplitz operators with unbounded symbolsAuthors: Joseph A. Cima (1) and Željko Čučković (2)
Author institution: (1) Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA
(2) Department of Mathematics, The University of Toledo, Toledo, OH 43606-3390, USA
Summary: We construct bounded Toeplitz operators on the Bergman space $L^2_a$ on the unit disk, whose symbols are unbounded functions. These operators can be compact and in some cases Hilbert-Schmidt. In fact we show that for any essentially unbounded function $H \in L^2$ there is a set $\Gamma$ in the unit disk such that the essentially unbounded function given by $h=\chi_{\Gamma}H$ is the symbol for a compact Toeplitz operator on $L^2_a$.
Keywords: Toeplitz operators, compact operators, Hilbert-Schmidt operators.
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