Spectral Properties of Generalized Ces�ro Operators

We investigate spectral properties of operators on H2 of the form $$ \mathcal{C}_g (f)(z) = \frac{1} {z}\int\limits_0^z {f(t)g(t)dt} . $$ We describe the fine spectrum when g is a rational function. We also provide useful relations for these operators in the Calkin algebra.