Publication Date:
2013-11-27
Description:
The curvature K T ( w ) of a contraction T in the Cowen–Douglas class B 1 (D) is bounded above by the curvature K S * ( w ) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, 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 T corresponding to the operator T in the Cowen–Douglas class B 1 (D) which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B 1 () for a bounded domain in C m .
Print ISSN:
0024-6107
Electronic ISSN:
1469-7750
Topics:
Mathematics
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