Quasi doubly stochastic operator on l 1 and Nielsen’s theorem

In this paper, we introduce the quasidoubly stochastic operator, which is between doubly stochastic operators and column stochastic operators, so as to apply to characterized operator S on l1 such that Sf is majorized by f for every f ∈ l1. We present some classes of majorization preservers on l1 under quasi doubly stochastic operators. Moreover, as an application of our result in quantum physics, the convertibility of pure states of a composite system by local operations and classical communication has been considered.