Linear Preservers of Chain Majorization
For (n×m matrices) X, Y ∈ Mnm(R)(= Mnm), we say X is chain majorized by Y and write X ≺≺ Y if X = RY where R is a product of finitely many T-transforms. A linear operator T : Mnm → Mnm is said to be a linear preserver of the relation ≺≺ on Mnm if X ≺≺ Y implies that T X ≺≺ T Y . Also, it is said...
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| Format: | Article |
| Language: | English |
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Islamic Azad University
2008-03-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/35 |
| Summary: | For (n×m matrices) X, Y ∈ Mnm(R)(= Mnm), we say
X is chain majorized by Y and write X ≺≺ Y if X = RY where
R is a product of finitely many T-transforms. A linear operator
T : Mnm → Mnm is said to be a linear preserver of the relation ≺≺
on Mnm if X ≺≺ Y implies that T X ≺≺ T Y . Also, it is said to
be strong linear preserver if X ≺≺ Y is equivalent to T X ≺≺ T Y .
In this paper we characterize linear and strong linear preservers of
≺≺ |
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| ISSN: | 1735-8299 1735-8299 |