Perturbation theoretic entropy of the boundary actions of free groups
HTML articles powered by AMS MathViewer
- by Rui Okayasu PDF
- Proc. Amer. Math. Soc. 134 (2006), 1771-1776 Request permission
Abstract:
We compute the exact value of Voiculescu’s perturbation theoretic entropy of the boundary actions of free groups. This result is a partial answer of Voiculescu’s question.References
- Andrzej Biś and PawełG. Walczak, Entropies of hyperbolic groups and some foliated spaces, Foliations: geometry and dynamics (Warsaw, 2000) World Sci. Publ., River Edge, NJ, 2002, pp. 197–211. MR 1882770, DOI 10.1142/9789812778246_{0}009
- A. Connes and E. Størmer, Entropy for automorphisms of $II_{1}$ von Neumann algebras, Acta Math. 134 (1975), no. 3-4, 289–306. MR 454657, DOI 10.1007/BF02392105
- Guy David and Dan Voiculescu, $s$-numbers of singular integrals for the invariance of absolutely continuous spectra in fractional dimensions, J. Funct. Anal. 94 (1990), no. 1, 14–26. MR 1077543, DOI 10.1016/0022-1236(90)90026-H
- Alessandro Figà-Talamanca and Massimo A. Picardello, Spherical functions and harmonic analysis on free groups, J. Functional Analysis 47 (1982), no. 3, 281–304. MR 665019, DOI 10.1016/0022-1236(82)90108-2
- Kengo Matsumoto, On $C^*$-algebras associated with subshifts, Internat. J. Math. 8 (1997), no. 3, 357–374. MR 1454478, DOI 10.1142/S0129167X97000172
- Rui Okayasu, Entropy of subshifts and the Macaev norm, J. Math. Soc. Japan 56 (2004), no. 1, 177–191. MR 2027621, DOI 10.2969/jmsj/1191418701
- Okayasu, R. Gromov hyperbolic groups and the Macaev Norm. Preprint.
- Dan Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators, J. Operator Theory 2 (1979), no. 1, 3–37. MR 553861
- Dan Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators. II, J. Operator Theory 5 (1981), no. 1, 77–100. MR 613049
- Dan Voiculescu, On the existence of quasicentral approximate units relative to normed ideals. I, J. Funct. Anal. 91 (1990), no. 1, 1–36. MR 1054113, DOI 10.1016/0022-1236(90)90047-O
- Dan Voiculescu, Entropy of dynamical systems and perturbations of operators, Ergodic Theory Dynam. Systems 11 (1991), no. 4, 779–786. MR 1145622, DOI 10.1017/S0143385700006489
- Dan Voiculescu, Entropy of dynamical systems and perturbations of operators. II, Houston J. Math. 17 (1991), no. 4, 651–661. MR 1147278
- Dan Voiculescu, Entropy-invariants of dynamical systems and perturbations of operators, Mathematical physics, X (Leipzig, 1991) Springer, Berlin, 1992, pp. 303–307. MR 1386418
Additional Information
- Rui Okayasu
- Affiliation: Department of Mathematics Education, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
- Email: rui@cc.osaka-kyoiku.ac.jp
- Received by editor(s): October 25, 2004
- Received by editor(s) in revised form: January 25, 2005
- Published electronically: December 15, 2005
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1771-1776
- MSC (2000): Primary 46L55; Secondary 28D20, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-05-08190-6
- MathSciNet review: 2207492