Some properties of right and left g-majorization on M_{n, m}
by
Ali Armandnejad
Department of Mathematics, Valiasr University of Rafsanjan, 7713936417, Rafsanjan, Iran.

Let M_{n, m} be the set of all n×m real matrices. A matrix R ∈ M_n with the property Re=e, is said to be a g-row stochastic matrix where e=(1, ..., 1) ∈ Fⁿ. A matrix D ∈ M_n with the property De=e and D^te=e, is said to be a g-doubly stochastic matrix. Let A, B ∈ M_{n, m}, so B is said to be left gw-majorized (gs-majorized) by A if there exists an n×n g-row ( g-doubly) stochastic matrix R such that B=RA. Let ~ be a relation on M_{n, m} and T be a linear operator on M_{n, m}, it is said that T preserves (or strongly preserves) ~ if TA ~ TB whenever A ~ B (or TA ~ TB if and only if A ~ B). In this paper we characterize all linear operators that strongly preserve g-majorization on M_{n, m}.

Date received: May 4, 2008