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Mat. Sb., 2019, Volume 210, Number 9, Pages 89–106 (Mi msb9130)  

Algebras of free holomorphic functions and localizations

K. A. Syrtseva

Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia

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.

Keywords: localization, free analytic algebra, Arens-Michael free product, algebra of holomorphic functions on a free polydisc, algebra of holomorphic functions on a free ball.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
This research was carried out within the HSE University Basic Research Program and funded (jointly) by the Russian Academic Excellence Project ‘5-100’.


DOI: https://doi.org/10.4213/sm9130

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English version:
Sbornik: Mathematics, 2019, 210:9, 1288–1304

Bibliographic databases:

UDC: 517.986.2
MSC: Primary 46H05; Secondary 47A60, 46H25
Received: 01.05.2018 and 29.01.2019

Citation: K. A. Syrtseva, “Algebras of free holomorphic functions and localizations”, Mat. Sb., 210:9 (2019), 89–106; Sb. Math., 210:9 (2019), 1288–1304

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