Linear Maps which Preserve or Strongly Preserve Weak Majorization
For x,y∈â„Ân, we say x is weakly submajorized (weakly supermajorized) by y, and write x≺Éy (x≺Éy), 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↓...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-02-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/82910 |
| _version_ | 1811215735119151104 |
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| author | Mohammad Ali Vali Ahmad Mohammad Hasani |
| author_facet | Mohammad Ali Vali Ahmad Mohammad Hasani |
| author_sort | Mohammad Ali Vali |
| collection | DOAJ |
| description | For x,y∈â„Ân, we say x is weakly submajorized (weakly supermajorized) by y, and write x≺Éy (x≺Éy), 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 ≺É or ≺É. |
| first_indexed | 2024-04-12T06:27:18Z |
| format | Article |
| id | doaj.art-b66552b109404fa3a211d9bd13633b13 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-12T06:27:18Z |
| publishDate | 2008-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-b66552b109404fa3a211d9bd13633b132022-12-22T03:44:06ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2008-02-01200710.1155/2007/82910Linear Maps which Preserve or Strongly Preserve Weak MajorizationMohammad Ali ValiAhmad Mohammad HasaniFor x,y∈â„Ân, we say x is weakly submajorized (weakly supermajorized) by y, and write x≺Éy (x≺Éy), 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 ≺É or ≺É.http://dx.doi.org/10.1155/2007/82910 |
| spellingShingle | Mohammad Ali Vali Ahmad Mohammad Hasani Linear Maps which Preserve or Strongly Preserve Weak Majorization Journal of Inequalities and Applications |
| title | Linear Maps which Preserve or Strongly Preserve Weak Majorization |
| title_full | Linear Maps which Preserve or Strongly Preserve Weak Majorization |
| title_fullStr | Linear Maps which Preserve or Strongly Preserve Weak Majorization |
| title_full_unstemmed | Linear Maps which Preserve or Strongly Preserve Weak Majorization |
| title_short | Linear Maps which Preserve or Strongly Preserve Weak Majorization |
| title_sort | linear maps which preserve or strongly preserve weak majorization |
| url | http://dx.doi.org/10.1155/2007/82910 |
| work_keys_str_mv | AT mohammadalivali linearmapswhichpreserveorstronglypreserveweakmajorization AT ahmadmohammadhasani linearmapswhichpreserveorstronglypreserveweakmajorization |