Generalized Cesàro Operators: Geometry of Spectra and Quasi-Nilpotency
For the class of Hardy spaces and standard weighted Bergman spaces of the unit disk, we prove that the spectrum of a generalized Cesàro operator Tg is unchanged if the symbol g is perturbed to g+h by an analytic function h inducing a quasi-nilpotent operator Th, that is, spectrum of Th equals {0}. We also show that any Tg operator that can be approximated in the operator norm by an operator Th w