On Linear Preservers of lgw-Majorization on Mn,m

Let Mn,m be the set of all n×m matrices with entries in F, where F is the field of real or complex numbers. For A, B∈Mn,m, we say that B is lgw-majorized (left generalized weakly majorized) by A if there exists an n×n g-row stochastic (generalized row stochastic) matrix R such that B=RA. In this paper, we characterize all linear operators that strongly preserve lgw-majorization on Mn,m and all linear operators that strongly preserve left weak matrix majorization on Mn.