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 $B$. 
@article{EMJ_2021_12_3_a4,
     author = {R. Hosseinzadeh},
     title = {Maps preserving the coincidence points of operators},
     journal = {Eurasian mathematical journal},
     pages = {42--45},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2021_12_3_a4/}
}
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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/