Geodesic
Maps preserving the coincidence points of operators
Eurasian mathematical journal, Tome 12 (2021) no. 3, pp. 42-45.

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Let $\mathcal{B(X)}$ be the algebra of all bounded linear operators on a Banach space $\mathcal{X}$ with $\dim \mathcal{X} \geqslant 2$. In this paper, we describe surjective maps $\phi: \mathcal{B(X)}\to\mathcal{B(X)}$ preserving the coincidence points of operators, i.e., $C(A,B)=C(\phi(A),\phi(B))$, for every $A, B \in \mathcal{B(X)}$, where $C(A,B)$ denotes the set of all coincidence points of two operators $A$ and $B$. 
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R. Hosseinzadeh. Maps preserving the coincidence points of operators. Eurasian mathematical journal, Tome 12 (2021) no. 3, pp. 42-45. http://geodesic.mathdoc.fr/item/EMJ_2021_12_3_a4/

[1] M. Abbas, G. Jungck, “Common xed point results for noncommuting mappings without continuity in cone metric spaces”, Journal of Mathematical Analysis and Applications, 341 (2008), 416–420 | DOI | Zbl

[2] H. Havlicek, P. Semrl, “From geometry to invertibility preservers”, Studia Mathematica, 174 (2006), 99–109 | DOI | Zbl

[3] A. Taghavi, R. Hosseinzadeh, E. Nasrollahi, “A characterization of an isomorphism”, Asian-European Journal of Mathematics, 11 (2018), 1850022, 9 pp. | DOI | Zbl

[4] A. Taghavi, R. Hosseinzadeh, H. Rohi, “Additive maps preserving idempotency of products or Jordan products of operators”, Iranian Journal of Mathematical Sciences and Informatics, 11 (2016), 131–137 | Zbl

[5] A. Taghavi, R. Hosseinzadeh, “Mappings on $C^*$-algebras preserving the sum of absolute values”, Linear and Multilinear Algebra, 66 (2018), 217–223 | DOI | Zbl

[6] A. Taghavi, R. Hosseinzadeh, “Maps preserving the dimension of fixed points of products of operators”, Linear and Multilinear Algebra, 62 (2014), 1285–1292 | DOI | Zbl

[7] A. Taghavi, R. Hosseinzadeh, H. Rohi, “Maps preserving the fixed points of sum of operators”, Operators and Matrices, 9 (2015), 563–569 | DOI | Zbl

[8] A. Taghavi, R. Hosseinzadeh, V. Darvish, “Maps preserving the fixed points of triple Jordan products of operators”, Indagationes Mathematicae, 27 (2016), 850–854 | DOI | Zbl

[9] P. Šemrl, “Two characterizations of automorphisms on B(X)”, Studia Mathematica, 105 (1993), 143–148 | DOI