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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 3 > No. 1

 
   

On Non-Commutative Weighted Ergodic Theorems for Multi-Parameter Semigroups

PP: 79-88
Author(s)
Abdusalom Karimov,
Abstract
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 ft1gt10; : : : ; ftN gtN0, 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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