RESEARCH ANNOUNCEMENTS ON“MAXIMAL ERGODIC INEQUALITIES FOR SOME POSITIVE OPERATORS ON NONCOMMUTATIVE LP-SPACE”

1 Introduction and Main Results In classical ergodic theory,one of the earliest pointwise ergodic convergence theorems was obtained by Birkhoff[1]in 1931.Dunford and Schwartz[2]greatly generalized the previous situation;they established the strong(p;p)maximal inequalities for all 1<p<∞ for time averages of positive L1-L∞ contractions and obtained the pointwise convergence result as a corollary.