A. È. Guterman, “Monotone Additive Matrix Transformations”, Mat. Zametki, 81:5 (2007), 681–692; Math. Notes, 81:5 (2007), 609

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Matematicheskie Zametki, 2007, Volume 81, Issue 5, Pages 681–692
DOI: https://doi.org/10.4213/mzm3713 (Mi mzm3713)

This article is cited in 12 scientific papers (total in 12 papers)

Monotone Additive Matrix Transformations

A. È. Guterman

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (478 kB) Citations (12)

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DOI: https://doi.org/10.4213/mzm3713

Abstract: We investigate additive transformations on the space of real or complex matrices that are monotone with respect to any admissible partial order relation. A complete characterization of these transformations is obtained. In the real case, we show that such transformations are linear and that all nonzero monotone transformations are bijective. As a corollary, we characterize all additive transformations that are monotone with respect to certain classical matrix order relations, in particular, with respect to the Drazin order, left and right

*

$*$ -orders, and the diamond order.

Keywords: matrix partial order, monotone transformation, partially ordered set, Lewner order, Hartwig order, Drazin order, diamond order.

Received: 07.06.2006
Revised: 22.11.2006

English version:
Mathematical Notes, 2007, Volume 81, Issue 5, Pages 609–619
DOI: https://doi.org/10.1134/S0001434607050057

Bibliographic databases:

UDC: 512.643

Language: Russian

Citation: A. È. Guterman, “Monotone Additive Matrix Transformations”, Mat. Zametki, 81:5 (2007), 681–692; Math. Notes, 81:5 (2007), 609–619

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm3713

https://doi.org/10.4213/mzm3713

https://www.mathnet.ru/eng/mzm/v81/i5/p681

This publication is cited in the following 12 articles:

Dolinar G., Marovt Bojan Kuzma Janko, Marovt J., Poon E., “One-Sided Star Partial Order Preservers on B(H)”, Oper. Matrices, 15:3 (2021), 1141–1159
Golubic I., Marovt J., “Preservers of Partial Orders on the Set of All Variance-Covariance Matrices”, Filomat, 35:2 (2021), 617–632
Dolinar G., Halicioglu S., Harmanci A., Kuzma B., Marovt J., Ungor B., “Preservers of the Left-Star and Right-Star Partial Orders”, Linear Alg. Appl., 587 (2020), 70–91
Golubic I., Marovt J., “Monotone Transformations on the Cone of All Positive Semidefinite Real Matrices”, Math. Slovaca, 70:3 (2020), 733–744
Golubic I., Marovt J., “Preservers of Partial Orders on the Set of All Variance-Covariance Matrices”, Filomat, 34:9 (2020), 3015–3030
Burgos M., Marquez-Garcia A.C., Morales-Campoy A., “Maps preserving the diamond partial order”, Appl. Math. Comput., 296 (2017), 137–147
A. E. Guterman, E. M. Kreines, Qing-Wen Wang, “Monotone linear transformations on matrices over semirings”, J. Math. Sci., 233:5 (2018), 675–686
Burgos M., Marquez-Garcia A.C., Patricio P., “on Mappings Preserving the Sharp and Star Orders”, Linear Alg. Appl., 483 (2015), 268–292
Dolinar G., Guterman A., Marovt J., “Monotone Transformations on B(H) With Respect To the Left-Star and the Right-Star Partial Order”, Math. Inequal. Appl., 17:2 (2014), 573–589
Dolinar G., Guterman A., Marovt J., “Automorphisms of K(H) with Respect to the Star Partial Order”, Oper. Matrices, 7:1 (2013), 225–239
A. E. Guterman, M. A. Efimov, “Monotone maps on matrices of index one”, J. Math. Sci. (N. Y.), 191:1 (2013), 36–51
Orel M., Kuzma B., “Additive rank-one nonincreasing maps on Hermitian matrices over the field $\mathrm{GF}(2^2)$ ”, Electron. J. Linear Algebra, 18 (2009), 482–499

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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