Resumen de Commutator lifting inequalities and interpolation

Gelu Popescu

• In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. This inequality yields a multivariable lifting theorem that generalizes the noncommutative commutant lifting theorem. This is then used to solve new operator-valued interpolation problems of Schur¿Carathéodory, Nevanlinna¿Pick, and Sarason type on Fock spaces. Some consequences to norm constrained analytic interpolation in the unit ball of Cn are also considered.