On Linear Maps Preserving g-Majorization from <inline-formula> <graphic file="1029-242X-2010-254819-i1.gif"/></inline-formula> to <inline-formula> <graphic file="1029-242X-2010-254819-i2.gif"/></inline-formula>

Abstract

Let and be the usual spaces of n-dimensional column and m-dimensional row vectors on , respectively, where is the field of real or complex numbers. In this paper, the relations gs-majorization, lgw-majorization, and rgw-majorization are considered on and . Then linear maps preserving lgw-majorization or gs-majorization and linear maps , preserving rgw-majorization are characterized.