Open Access

Linear Maps which Preserve or Strongly Preserve Weak Majorization

Journal of Inequalities and Applications20082007:082910

DOI: 10.1155/2007/82910

Received: 8 July 2007

Accepted: 5 November 2007

Published: 6 February 2008

Abstract

For , we say is weakly submajorized (weakly supermajorized) by , and write , if , where denotes the th component of the vector whose components are a decreasing (increasing) rearrangment of the components of . We characterize the linear maps that preserve (strongly preserve) one of the majorizations or .

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Authors’ Affiliations

(1)
Department of Mathematics, Shahid Bahonar University of Kerman

Copyright

© A. M. Hasani and M. A. Vali 2007

This article is published under license to BioMed Central Ltd. 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.