Free pluriharmonic majorants and noncommutative interpolation
Abstract
In this paper, we initiate the study of sub-pluriharmonic curves in Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative balls. We are lead to a characterization of the noncommutative Hardy space H2 ball in terms of free pluriharmonic majorants, and to a Schur type description of the unit ball of H2 ball. These results are used to solve a multivariable commutant lifting problem and provide a description of all solutions.
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