Let be a sequence of arbitrary random variables with and , for every and be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence...

In this paper, we prove the analogue of classical strong and weak symmetrization maximal inequalities in the noncommutative setup. As an application, we give a relation between sure convergence of a series of jointly independent random variables...