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August 2019 Curvature inequalities and extremal operators
Gadadhar Misra, Md. Ramiz Reza
Illinois J. Math. 63(2): 193-217 (August 2019). DOI: 10.1215/00192082-7768711

Abstract

A curvature inequality is established for contractive commuting tuples of operators T in the Cowen–Douglas class Bn(Ω) of rank n defined on some bounded domain Ω in Cm. Properties of the extremal operators (that is, the operators which achieve equality) are investigated. Specifically, a substantial part of a well-known question due to R. G. Douglas involving these extremal operators, in the case of the unit disc, is answered.

Citation

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Gadadhar Misra. Md. Ramiz Reza. "Curvature inequalities and extremal operators." Illinois J. Math. 63 (2) 193 - 217, August 2019. https://doi.org/10.1215/00192082-7768711

Information

Received: 26 December 2016; Revised: 3 April 2019; Published: August 2019
First available in Project Euclid: 1 August 2019

zbMATH: 07088305
MathSciNet: MR3987495
Digital Object Identifier: 10.1215/00192082-7768711

Subjects:
Primary: 30C40
Secondary: 47A13, 47A25

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 2 • August 2019
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