Ergodic actions of convergent Fuchsian groups on quotients of the noncommutative Hardy algebras

Arias, Alvaro; Latrémolière, Frédéric

doi:10.1090/S0002-9939-2011-10794-9

Ergodic actions of convergent Fuchsian groups on quotients of the noncommutative Hardy algebras

Authors: Alvaro Arias and Frédéric Latrémolière
Journal: Proc. Amer. Math. Soc. 139 (2011), 2485-2496
MSC (2010): Primary 47L15, 47L55; Secondary 32M05
DOI: https://doi.org/10.1090/S0002-9939-2011-10794-9
Published electronically: January 4, 2011
MathSciNet review: 2784814
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Abstract: We establish that particular quotients of the noncommutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group $\operatorname*{SU}(n,1)$ of automorphisms of the unit ball in $\mathbb{C}^{n}$ . To do so, we provide a mean to compute the spectra of quotients of noncommutative Hardy algebra and characterize their automorphisms in terms of biholomorphic maps of the unit ball in $\mathbb{C}^{n}.$

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Additional Information

Alvaro Arias
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: aarias@math.du.edu

Frédéric Latrémolière
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: frederic@math.du.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10794-9
Keywords: Noncommutative Hardy algebras, Fock spaces, Fuchsian group, Mobius transformations, automorphisms of operator algebras.
Received by editor(s): March 2, 2010
Received by editor(s) in revised form: June 30, 2010
Published electronically: January 4, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.