Commutator lifting inequalities and interpolation

• Autores: Gelu Popescu
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 225, Nº 1, 2006, págs. 155-176
• Idioma: inglés
• DOI: 10.2140/pjm.2006.225.155
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• Resumen

  • 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.