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A polynomial approximation result for free Herglotz-Agler functions (2203.14243v2)
Published 27 Mar 2022 in math.FA, math.CV, and math.OA
Abstract: In this paper, we prove a noncommutative (nc for short) analog of Schwarz lemma for the nc Schur-Agler class and prove that the regular nc Schur-Agler class and the regular free Herglotz class are homeomorphic. Moreover, we give a characterization of regular free Herglotz functions. As an application, we will show that any regular free Herglotz functions can uniformly be approximated by regular Herglotz free polynomials.