Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 254819, 5 pages
doi:10.1155/2010/254819
Research Article

On Linear Maps Preserving g-Majorization from 𝔽n to 𝔽m

Ali Armandnejad and Hossein Heydari

Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran

Received 5 October 2009; Revised 7 January 2010; Accepted 16 February 2010

Academic Editor: Jong Kim

Copyright © 2010 Ali Armandnejad and Hossein Heydari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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