Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Individual ergodic theorem for unitary maps of random matrices

Author(s): Ryszard Jajte
Journal: Proc. Amer. Math. Soc. 132 (2004), 2475-2481.
MSC (2000): Primary 60F15, 46L10
Posted: March 25, 2004
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Using simple techniques of finite von Neumann algebras, we prove a limit theorem for random matrices.

References:

[1]
Charn Huen Kan, Ergodic properties of Lamperti operators, Canad. J. Math. 30 (1978), 1206-1214. MR 80g:47037

[2]
A. de la Torre, A simple proof of the maximal ergodic theorem, Canad. J. Math. 28 (1976), 1073-1075. MR 54:5867

[3]
J. Dixmier, Formes linéaires sur un anneau d'opérateurs, Bull. Soc. Math. France 81 (1953), 9-39. MR 15:539a

[4]
R. Duncan, Some pointwise convergence results in $L^{p}(\mu )$, $1<p<\infty $, Canad. Math. Bull. 20 (1977), 277-284. MR 58:17038

[5]
R. Duncan, Pointwise convergence theorems for self-adjoint and unitary contractions, Ann. Prob. 5 (1977), 622-626. MR 56:3247

[6]
A. Ionescu Tulcea, Ergodic properties of isometries in $L^{p}$ spaces, $1<p<\infty $, Bull. Amer. Math. Soc. 70 (1964), 366-371. MR 34:6026

[7]
R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes in Math. 1110, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. MR 86e:46058

[8]
R. Jajte, Strong Limit Theorems in Noncommutative $L^{2}$-spaces, Lecture Notes in Math. 1477, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1991. MR 92h:46091

[9]
E. Nelson, Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103-116. MR 50:8102

[10]
I. E. Segal, A non-commutative extension of abstract integration, Ann. Math. 57 (1953), 401-457; erratum, ibid. 58 (1953), 595-596. MR 14:991f; MR 15:204h

[11]
E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. Math. Studies 63, Princeton University Press, Princeton, New Jersey, 1970. MR 40:6176

[12]
S. Stratila and L. Zsido, Lectures on von Neumann Algebras, Editura Academiei, Bucuresti and Abacus Press, Turnbridge Wells, 1979. MR 81j:46089

[13]
F. J. Yeadon, Ergodic theorems for semifinite von Neumann algebras I, J. London Math. Soc. 2 (16) (1977), 326-332. MR 58:7111

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60F15, 46L10

Retrieve articles in all Journals with MSC (2000): 60F15, 46L10

Additional Information:

Ryszard Jajte
Affiliation: Faculty of Mathematics, University of Lódz, Banacha 22, PL-90-238 Lódz, Poland
Email: rjajte@math.uni.lodz.pl

DOI: 10.1090/S0002-9939-04-07388-5
PII: S 0002-9939(04)07388-5
Keywords: Random matrix, positive isometry, ergodic theorem, von Neumann algebra
Received by editor(s): August 12, 2002
Received by editor(s) in revised form: February 26, 2003
Posted: March 25, 2004
Communicated by: Andreas Seeger
Copyright of article: Copyright 2004, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google