A Note on a Subclass of Cowen-Douglas Operators

Abstract

In this note, we study a rich operator class denoted by $${\cal P}{{\cal B}_n}({\rm{\Omega}})$$ which includes all homogeneous operators and quasi-homogeneous operators in the Cowen-Douglas class. A complete unitarily classification theorem is given. Furthermore, we also concern the curvature and similarity of operators in $${\cal P}{{\cal B}_n}({\rm{\Omega}})$$ .