INEQUALITIES FOR SUMS OF RANDOM VARIABLES IN NONCOMMUTATIVE PROBABILITY SPACES

摘要

In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter 1 <= r <= 2 and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative Hoeffding inequality as follows: Let (m,T) be a noncommutative probability space, Yt be a von Neumann subalgebra of m with the corresponding conditional expectation E-n. and let subalgebras n subset of u(j) subset of m(j = 1,...,n,) be successively independent over n. Let x(j) is an element of x(j) be self-adjoint such that a(i) <= x(j) <= b(j) for some real numbers a(j) < b(j) and E-n(x(j)) = mu it for some mu >= 0 and all 1 <= j <= n. Then for any t > o it holds that