A note on curvature and similarity of some Cowen–Douglas operators

The purpose of this note is to describe the similarity of Cowen–Douglas operators with index one by considering the difference of the curvatures of the corresponding vector bundles. We define a subclass of operators of B1(D)B1(D) that includes the weighted shift operators with weighted sequence {[(k+1)(k+α)]1/2}k=0∞, α≥1α≥1 and consider when an operator in B1(D)B1(D) is similar to some operator in this operator class.