Journal of Operator Theory

Volume 38, Issue 1, Summer 1997 pp. 19-24.

A class of operators associated with reproducing kernels

Authors: Kehe Zhu
Author institution:Department of Mathematics, State University of New York, Albany, NY 12222, USA, E-mail: kzhu@math.albany.edu

Summary: For t > 0 let $A_t$ be the operator on $l^2$ whose matrix under the standard basis has as its (i, j) entry $(1 - \left| {z_i } \right|^2 )^{t/2} (1 - \left| {z_j } \right|^2 )^{t/2} (1 - z_i \bar z_j )^{ - t}$. Here ${z_n}$ is a sequence of points in the open unit disk in the complex plane. The boundedness of the operators $A_t$, $1 \leqslant t < \infty$, will be characterized in terms of the distribution of the sequence ${z_n}$ in the hyperbolic metric.

Keywords: Reproducing kernel, separated sequences, Carleson measures.

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