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Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

Biswas, Shibananda and Keshari, Dinesh Kumar and Misra, Gadadhar (2013) Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class. In: Journal of the London Mathematical Society, 88 (3). pp. 941-956.

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Official URL: http://dx.doi.org/10.1112/jlms/jdt045

Abstract

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (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() 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.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Oxford University Press.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 09 Jan 2014 08:25
Last Modified: 09 Jan 2014 08:25
URI: http://eprints.iisc.ac.in/id/eprint/48104

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