Illinois Journal of Mathematics

Curvature inequalities and extremal operators

Gadadhar Misra and Md. Ramiz Reza

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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.

Article information

Illinois J. Math., Volume 63, Number 2 (2019), 193-217.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C40: Kernel functions and applications
Secondary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.) 47A25: Spectral sets


Misra, Gadadhar; Reza, Md. Ramiz. Curvature inequalities and extremal operators. Illinois J. Math. 63 (2019), no. 2, 193--217. doi:10.1215/00192082-7768711.

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