Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 63, Number 2 (2019), 193-217.
Curvature inequalities and extremal operators
A curvature inequality is established for contractive commuting tuples of operators in the Cowen–Douglas class of rank defined on some bounded domain in . 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.
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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Misra, Gadadhar; Reza, Md. Ramiz. Curvature inequalities and extremal operators. Illinois J. Math. 63 (2019), no. 2, 193--217. doi:10.1215/00192082-7768711. https://projecteuclid.org/euclid.ijm/1564646431