Geodesic
Infinite distohastic square operators in~$l_1$
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 76 (2022), pp. 20-31

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The article is devoted to bistochastic quadratic operators. The concept of a bistochastic quadratic operator is introduced and the property of such operators is studied. A necessary and sufficient condition for bistochasticity is given. An analogue of Birkhoff's theorem is studied for the class of bistochastic quadratic operators. A sufficient condition for the extremity of bistochastic quadratic operators is obtained, and a necessary condition is also obtained for small dimensions. The concept of bistochastic quadratic operators is generalized, and the concept of a bistochastic operator of arbitrary order is introduced.
Keywords: bistochastic quadratic operator, infinite-dimensional bistochastic quadratic operator, extreme points of the set of bistochastic matrices. 
@article{VTGU_2022_76_a1,
     author = {A. A. Imomov and A. I. Eshniyazov},
     title = {Infinite distohastic square operators in~$l_1$},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {20--31},
     publisher = {mathdoc},
     number = {76},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_76_a1/}
}
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A. A. Imomov; A. I. Eshniyazov. Infinite distohastic square operators in~$l_1$. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 76 (2022), pp. 20-31. http://geodesic.mathdoc.fr/item/VTGU_2022_76_a1/