Comptes Rendus
no. 11-12
Functional Analysis
Classification of noncommutative domain algebras
[Classification des algèbres de domaines noncommutatifs]

Présenté par : Gilles Pisier

Alvaro Arias1 ; Frédéric Latrémolière1
1 Department of Mathematics, University of Denver, Denver, CO 80208, USA
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 609-611.

Les algèbres de domaines noncommutatifs sont des analogues des algèbres de functions holomorphes sur un domaine défini par des inéquations polynômiales dans Cn. Elles généralisent également les algèbres de Hardy. Nous présentons dans cette Note la classification complète de ces algèbres, obtenue par des méthodes inspirées de lʼétude des functions biholomorphes entre domaines dʼespaces hermitiens.

Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of Cn defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete classification of these algebras based upon techniques inspired by multivariate complex analysis, and more specifically the classification of domains in hermitian spaces up to biholomorphic equivalence.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2012.06.003

Alvaro Arias 1 ; Frédéric Latrémolière 1

1 Department of Mathematics, University of Denver, Denver, CO 80208, USA 
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Alvaro Arias; Frédéric Latrémolière. Classification of noncommutative domain algebras. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2012.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.06.003/

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  • Jeet Sampat; Orr Moshe Shalit On the classification of function algebras on subvarieties of noncommutative operator balls, Journal of Functional Analysis, Volume 288 (2025) no. 2, p. 110703 | DOI:10.1016/j.jfa.2024.110703
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