Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 82910, 4 pages
Research Article

Linear Maps which Preserve or Strongly Preserve Weak Majorization

Ahmad Mohammad Hasani and Mohammad Ali Vali

Department of Mathematics, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran

Received 8 July 2007; Accepted 5 November 2007

Academic Editor: Jewgeni H. Dshalalow

Dedicated to Professor Mehdi Radjabalipour

Copyright © 2007 Ahmad Mohammad Hasani and Mohammad Ali Vali. 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.


For x,yn, we say x is weakly submajorized (weakly supermajorized) by y, and write xωy (xωy), if 1kx[i]1ky[i], k=1,2,,n (1kx(i)1ky(i), k=1,2,,n), where x[i] (x(i)) denotes the ith component of the vector x (x) whose components are a decreasing (increasing) rearrangment of the components of x. We characterize the linear maps that preserve (strongly preserve) one of the majorizations ω or ω.