Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T21:40:51.441Z Has data issue: false hasContentIssue false
  • English
  • Français

A MEAN ERGODIC THEOREM FOR ACTIONS OF AMENABLE QUANTUM GROUPS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  01 August 2008

ROCCO DUVENHAGE
ROCCO DUVENHAGE*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove a weak form of the mean ergodic theorem for actions of amenable locally compact quantum groups in the von Neumann algebra setting.

Keywords

mean ergodic theoremamenable quantum groupsvon Neumann algebras

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 87 - 95
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics, 2nd edn, Vol. 1 (Springer, New York, 1987).CrossRefGoogle Scholar
[2]de Beer, R., Duvenhage, R. and Ströh, A., ‘Noncommutative recurrence over locally compact Hausdorff groups’, J. Math. Anal. Appl. 322 (2006), 66–74.CrossRefGoogle Scholar
[3]Desmedt, P., Quaegebeur, J. and Vaes, S., ‘Amenability and the bicrossed product construction’, Illinois J. Math. 46 (2002), 1259–1277.CrossRefGoogle Scholar
[4]Enock, M. and Schwartz, J.-M., Kac Algebras and Duality of Locally Compact Groups (Springer, Berlin, 1992).CrossRefGoogle Scholar
[5]Krengel, U., Ergodic Theorems (Walter de Gruyter and Co., Berlin, 1985).CrossRefGoogle Scholar
[6]Kustermans, J. and Vaes, S., ‘A simple definition for locally compact quantum groups’, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), 871–876.CrossRefGoogle Scholar
[7]Kustermans, J. and Vaes, S., ‘The operator algebra approach to quantum groups’, Proc. Natl Acad. Sci. USA 97 (2000), 547–552.CrossRefGoogle ScholarPubMed
[8]Kustermans, J. and Vaes, S., ‘Locally compact quantum groups’, Ann. Sci. École Norm. Sup. (4) 33 (2000), 837–934.CrossRefGoogle Scholar
[9]Kustermans, J. and Vaes, S., ‘Locally compact quantum groups in the von Neumann algebraic setting’, Math. Scand. 92 (2003), 68–92.CrossRefGoogle Scholar
[10]Paterson, A. L. T., ‘Amenability’, in: Mathematical Surveys and Monographs, Vol. 29 (American Mathematical Society, Providence, RI, 1988).Google Scholar
[11]Petersen, K., Ergodic Theory (Cambridge University Press, Cambridge, 1983).CrossRefGoogle Scholar
[12]Sakai, S., C*-algebras and W*-algebras (Springer, Berlin, 1998), reprint of the 1971 edition.CrossRefGoogle Scholar
[13]Strătilă, Ş., Modular Theory in Operator Algebras (Editura Academiei Republicii Socialiste România, Abacus Press, Bucharest, Tunbridge Wells, 1981), translated from the Romanian by the author.Google Scholar
[14]Vaes, S., ‘The unitary implementation of a locally compact quantum group action’, J. Funct. Anal. 180 (2001), 426–480.CrossRefGoogle Scholar