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A polynomial approximation result for free Herglotz–Agler functions

Part of: Selfadjoint operator algebras Holomorphic functions of several complex variables

Published online by Cambridge University Press:  17 October 2022

Kenta Kojin
Kenta Kojin*
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
*
e-mail: m20016y@math.nagoya-u.ac.jp
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Abstract

In this paper, we prove a noncommutative (nc) analog of Schwarz lemma for the nc Schur–Agler class and prove that the regular nc Schur–Agler class and the regular free Herglotz–Agler class are homeomorphic. Moreover, we give a characterization of regular free Herglotz–Agler functions. As an application, we will show that any regular free Herglotz–Agler functions can uniformly be approximated by regular Herglotz–Agler free polynomials.

Keywords

Schwarz lemmanc Schur–Agler classfree Herglotz–Agler class

MSC classification

Primary: 32A70: Functional analysis techniques 46L52: Noncommutative function spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 2 , June 2023 , pp. 665 - 678
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

The author would like to take this opportunity to thank the “Nagoya University Interdisciplinary Frontier Fellowship” supported by JST and Nagoya University.

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