Journal of Operator Theory

Volume 52, Issue 2, Fall 2004 pp. 341-351.

Generalized Cesaro operators and the Bergman space

Authors: Scott W. Young
Author institution: University Of South Carolina, Department of Mathematics, Columbia, SC 29208, USA

Summary: We investigate spectral properties of operators on $L_a^2$ of the form $$ {\cal C}_g(f)(z) = \frac{1}{z} \int\limits_0^z f(t) g(t) {\rm d}t.$$ We compute the spectrum when $g$ is a rational function, as well as the essential spectrum and the Fredholm index. We also provide relations for these operators in the Calkin algebra.

Keywords: We investigate spectral properties of operators on $L_a^2$ of the form $$ {\C}_g(f)(z) = \frac{1}{z} \int\limits_0^z f(t) g(t) {\rm d}t.$$ We compute the spectrum when $g$ is a rational function, as well as the essential spectrum and the Fredholm index. We also provide relations for these operators in the Calkin algebra.

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