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A refined nc Oka–Weil theorem

Part of: Basic linear algebra

Published online by Cambridge University Press:  02 November 2021

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

This short note refines a noncommutative (nc) Oka–Weil theorem by using a characterization of free compact nc sets based on the notion of dilation hulls. A consequence of it is that any free holomorphic function can be represented as a free polynomial on each free compact nc set.

Keywords

nc Oka–Weil theoremnc functionsfree holomorphic functions

MSC classification

Primary: 15A54: Matrices over function rings in one or more variables
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 218 - 224
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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