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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
Published electronically:
January 4, 2011
MathSciNet review:
2784814
Full-text PDF
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Additional Information
Abstract: We establish that particular quotients of the noncommutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group  of automorphisms of the unit ball in  . 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 
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- 1.
- A. Arias and F. Latrémoliere, Isomorphisms of non-commutative domain algebras, to appear in J. Oper. Theory.
- 2.
- W. Arveson, Subalgebras of
 -algebras. III. Multivariable operator theory, Acta Math. 181 (1998), no. 2, 159-228. MR 1668582 (2000e:47013)
- 3.
- K. Davidson and D. Pitts, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275-303. MR 1625750 (2001c:47082)
- 4.
- -, Invariant subspaces and hyper-reflexivity for free semigroup algebras, Proc. London Math. Soc. (3) 78 (1999), no. 2, 401-430. MR 1665248 (2000k:47005)
- 5.
- S. Krantz, Function theory of several complex variables, Mathematics Series, Wadsworth and Brooks/Cole, 1992.
- 6.
- -, Handbook of complex variables, Birkhäuser, Boston, MA, 1999. MR 1738432 (2001a:30001)
- 7.
- G. Popescu, Von Neumann inequality for
 , Math. Scand. 68 (1991), no. 2, 292-304. MR 1129595 (92k:47073)
- 8.
- -, Non-commutative disc algebras and their representations, Proc. Amer. Math. Soc. 124 (1996), no. 7, 2137-2148. MR 1343719 (96k:47077)
- 9.
- -, Poisson transforms on some
 -algebras generated by isometries, J. Funct. Anal. 161 (1999), no. 1, 27-61. MR 1670202 (2000m:46117)
- 10.
- -, Operator theory on noncommutative domains, Mem. Amer. Math. Soc. 205 (2010), no. 964, vi + 124 pp.
- 11.
- -, Free holomorphic automorphisms of the unit ball of
 , J. Reine Angew. Math. 638 (2010), 119-168. MR 2595338
- 12.
- W. Rudin, Function theory in the unit ball of
 , Grundlehren der Mathematischen Wissenschaften, vol. 241, Springer-Verlag, 1980. MR 0601594 (82i:32002)
- 13.
- D. Voiculescu, Symmetries of some reduced free product
 -algebras, Lecture Notes in Mathematics, vol. 1132, Springer-Verlag, Berlin, 1985. MR 799593 (87d:46075)
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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:
http://dx.doi.org/10.1090/S0002-9939-2011-10794-9
PII:
S 0002-9939(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.
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