Email this article Algebras of free holomorphic functions and localizations
- Authors: Syrtseva K.A.1
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Affiliations:
- Department of Mathematics, National Research University "Higher School of Economics"
- Issue: Vol 210, No 9 (2019)
- Pages: 89-106
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133286
- DOI: https://doi.org/10.4213/sm9130
- ID: 133286
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Abstract
We consider the algebras of holomorphic functions on a free polydisc $\mathscr F^T(\mathbb D_R^n)$, $\mathscr F(\mathbb D_R^n)$ and the algebra of holomorphic functions on a free ball $\mathscr F(\mathbb B_r^n)$. We show that the algebra $\mathscr F(\mathbb D_R^n)$ is a localization of a free algebra and, moreover, is a free analytic algebra with $n$ generators (in the sense of J. Taylor), while the algebra $\mathscr F(\mathbb B_r^n)$ is not a localization of a free algebra. In addition we prove that the class of localizations of free algebras and the class of free analytic algebras are closed under the operation of the Arens-Michael free product. Bibliography: 21 titles.
About the authors
Ksenia Alexandrovna Syrtseva
Department of Mathematics, National Research University "Higher School of Economics"without scientific degree, no status
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