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Thursday, November 26, 2015 - 09:30 to 10:30
M 4
Dinesh Kumar Keshari
Indian Institute of Science Bangalore
Curvature inequalities for operators in the Cowen–Douglas class

The curvature of a contraction T in the Cowen-Douglasclass is bounded above by the curvature of the backward shiftoperator. However, in general, an operator satisfying thecurvature inequality need not be contractive. In this talk wecharacterize a slightly smaller class of contractions using astronger form of the curvature inequality.  Along the way, we findconditions on the metric of the holomorphic Hermitian vectorbundle E corresponding to the operator T in the Cowen-Douglasclass which ensures negative definiteness of the curvaturefunction. We obtain a generalization for commuting tuples ofoperators in the Cowen-Douglas class.

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