Curvature Inequalities and Extremal Operators
arXiv:1802.01386 · doi:10.1215/00192082-7768711
Abstract
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. 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.
19 pages