Continuous monotone maps on matrices for orders induced by the group inverse

Mikhail A. Efimov; Alexander E. Guterman

doi:10.7153/jmi-10-10

Continuous monotone maps on matrices for orders induced by the group inverse

Mikhail A. Efimov, Alexander E. Guterman

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

Abstract

We characterize continuous injective maps on the set of complex matrices which are monotone with respect to -order or order. In particular, we prove that all such maps must be automatically R-linear and surjective. We also present several examples of monotone maps showing that our assumptions are indispensable.

Original language	English
Pages (from-to)	123-133
Number of pages	11
Journal	Journal of Mathematical Inequalities
Volume	10
Issue number	1
DOIs	https://doi.org/10.7153/jmi-10-10
State	Published - 1 Mar 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Element, Zagreb.

Keywords

Group inverse
Matrix partial orders
Monotone matrix maps

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10.7153/jmi-10-10

Cite this

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Continuous monotone maps on matrices for orders induced by the group inverse

Abstract

Bibliographical note

Keywords

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