A note on commutativity preserving maps on M_n(ℝ)

Грегор Долинар, Bojan Kuzma, Janko Marovt

Type: Article

Publication Date: 2018-01-01

Citations: 0

DOI: https://doi.org/10.7153/oam-2018-12-07

View Chat PDF

Abstract

Let M n (F) be the set of all n × n matrices over a field F .Surjective maps which preserve the commutativity relation on M n (F) only in one direction have been recently classified for the case when F is an algebraically closed field.We show that the same result holds also when F = R is the field of real numbers and n 7 is odd.

Locations

Operators and Matrices - View - PDF

Similar Works

Action	Title	Year	Authors
+	Commutativity preserving linear maps and Lie automorphisms of strictly triangular matrix space	2002	You’an Cao Zhonghu Chen Chong Huang
+ PDF Chat	The group of commutativity preserving maps on strictly upper triangular matrices	2014	Dengyin Wang Min Zhu Jianling Rou
+	Strong commutativity preserving maps on subsets of matrices that are not closed under addition	2014	Cheng-Kai Liu
+	ADDITIVE COMMUTATIVITY PRESERVING MAPPINGS ON TRIANGULAR MATRIX ALGEBRAS	2004	Lichuan Jin
+	A note on idempotence-preserving maps	2008	Xiaomin Tang Jinli Xu Cao Chong-guang
+	Non-linear commutativity preserving maps on symmetric matrices	2007	Ajda Fošner
+ PDF Chat	Commuting maps on rank-k matrices	2014	Xiaowei Xu Xiaofei Yi
+	On maps preserving products equal to a diagonalizable matrix	2021	Louisa Catalano Hayden Julius
+	Maps on Matrix Algebras Preserving Commutativity	2004	Грегор Долинар Peter Šemrl
+ PDF Chat	On maps preserving products of matrices	2018	Louisa Catalano Samuel Hsu Regan Kapalko
+	On maps preserving products equal to a rank-one idempotent	2019	Louisa Catalano
+	Commutativity-preserving operators on symmetric matrices	1984	Heydar Radjavi
+	Commuting maps on some subsets of matrices that are not closed under addition	2012	Willian Franca
+	Commutativity preserving maps on M_n(R)	2009	Ajda Fošner
+	Maps from $M_n(\mathbb{F})$ to $\mathbb{F}$ that are multiplicative with respect to the Jordan triple product	2008	Mirko Dobovišek
+ PDF Chat	A note on commuting additive maps on rank k symmetric matrices	2021	Wai Leong Chooi Yean Nee Tan
+	A note on maps preserving products of matrices	2024	Lan Lu Yu Wang
+	Non-linear commutativity preserving maps on symetric matrices	2007	Ajda Fošner
+	Commuting maps on rank- k matrices	2012	Willian Franca
+	Commuting maps on rank-$k$ matrices	2012	Willian Franca

Cited by (0)

Action	Title	Year	Authors

Citing (8)

Action	Title	Year	Authors
+	Homomorphisms of commutativity relation	2015	Грегор Долинар Bojan Kuzma
+	Commutativity preserving maps	2007	Peter Šemrl
+	Reflexivity defect of spaces of linear operators	2008	Janko Bračič Bojan Kuzma
+	Linear maps preserving commutativity	1987	M. D. Choi Ali Jafarian Heydar Radjavi
+	Commutativity preserving maps on M_n(R)	2009	Ajda Fošner
+	A note on a conjecture about commuting graphs	2013	C. Miguel
+	On the diameter of the commuting graph of the full matrix ring over the real numbers	2017	J. M. Grau Antonio M. Oller‐Marcén C. Tasis
+	Functional Equations in Several Variables	1989	J. Aczél Jean Dhombres