Geodesic
Normality conditions for semilinear matrix operators of the Stein type
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 369-375

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Normality conditions are found for the operators associated with the semilinear analogs of the Stein matrix equation, namely, with the equations $X-A\overline XB=C$ and $X-AX^*B=C$. 
@article{SJVM_2015_18_4_a2,
     author = {Kh. D. Ikramov},
     title = {Normality conditions for semilinear matrix operators of the {Stein} type},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {369--375},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a2/}
}
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Kh. D. Ikramov. Normality conditions for semilinear matrix operators of the Stein type. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 369-375. http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a2/