Bergman spaces over noncommutative domains and commutant lifting

摘要

The goal of the present paper is to provide analogues of Sarason interpolation theorem in the Hardy algebra H-infinity(B) and Sz.Nagy-Foias commutant lifting theorem for contractions on Hilbert spaces in the setting of noncommutative Hardy spaces associated with noncommutative regular domains and varieties. This is accompanied by the study of multi-analytic operators with respect to the universal models associated with the regular domains (resp. varieties) and the study of multipliers of noncommutative Bergman spaces.