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 $H_{\mathbf{ball}}^2$ in terms of free pluriharmonic majorants, and to a Schur type description of the unit ball of $H_{\mathbf{ball}}^2$. These results are used to solve a multivariable commutant lifting problem and provide a description of all solutions.

35 pages