Title: Curvature inequalities for operators in the Cowen- Douglas class
Speaker: Mr. Dinesh Kumar Keshari
Date: 13 July 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall 1
The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this talk we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the Cowen-Douglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the Cowen-Douglas class.