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On Non-Commutative Weighted Ergodic Theorems for Multi-Parameter Semigroups |
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PP: 79-88 |
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Author(s) |
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Abdusalom Karimov,
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Abstract |
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| Mathematics Department, Institute of Textile and Light Industry, Tashkent, Uzbekistan
E-mail address: karimov57@rambler.ru
Received December 3, 2007; Revised August 17, 2008
In the present paper we consider a von Neumann algebra M with a faithful normal
semi-finite trace ? , and f®t1gt1¸0; : : : ; f®tN gtN¸0, N strongly continuous semigroups
of absolute contractions on Lp(M; ? ) (p > 1). We prove that for every
x 2 Lp(M; ? ) and Besicovitch function b(t1; : : : tN) the averages
1
T1T2 ¢ ¢ ¢ TN
Z TN
0
¢ ¢ ¢
Z T1
0
b(t1; : : : ; tN)(®tN ¢ ¢ ¢ ®t1 )(x)dt1dt2 ¢ ¢ ¢ dtN
converge b.a.u. in Lp(M) as maxfT1; : : : ; TNg ! 0 and minfT1; : : : ; TNg ! 1,
respectively. |
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