On the spectrum of the Cesàro operator on spaces of analytic functions

Abstract

This paper concerns the Cesàro operator acting on various spaces of analytic functions on the unit disc. The remarkable fact that this operator is subnormal when acting on the Hardy space H 2 has lead to extensive studies of its spectral picture on other spaces of this type. We present some of the methods that have been used to obtain information about the spectrum of the Cesàro operator acting on Hardy and Bergman spaces and give a unified approach to these problems which also yields new results in this direction. In particular, we prove that the Cesàro operator is subdecomposable on H 1 and on the standard weighted Bergman spaces L a 1 , α , α ⩾ 0 .