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

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

Keywords

Group inverse
Matrix partial orders
Monotone matrix maps

All Science Journal Classification (ASJC) codes

Analysis

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10.7153/jmi-10-10

Cite this

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title = "Continuous monotone maps on matrices for orders induced by the group inverse",

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.",

keywords = "Group inverse, Matrix partial orders, Monotone matrix maps",

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year = "2016",

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doi = "10.7153/jmi-10-10",

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AU - Efimov, Mikhail A.

AU - Guterman, Alexander E.

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PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - Group inverse

KW - Matrix partial orders

KW - Monotone matrix maps

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U2 - 10.7153/jmi-10-10

DO - 10.7153/jmi-10-10

M3 - مقالة

SN - 1846-579X

VL - 10

SP - 123

EP - 133

JO - Journal of Mathematical Inequalities

JF - Journal of Mathematical Inequalities

IS - 1

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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