Geodesic
On operators dominated by Kantorovich–Banach operators and Lévy operators in locally solid lattices
Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 3, pp. 55-61 
S. G. Gorokhova; E. Yu. Emelyanov. On operators dominated by Kantorovich–Banach operators and Lévy operators in locally solid lattices. Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 3, pp. 55-61. http://geodesic.mathdoc.fr/item/VMJ_2022_24_3_a3/
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     author = {S. G. Gorokhova and E. Yu. Emelyanov},
     title = {On operators dominated by {Kantorovich{\textendash}Banach} operators and {L\'evy} operators in locally solid lattices},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {55--61},
     year = {2022},
     volume = {24},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2022_24_3_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A linear operator $T$ acting in a locally solid vector lattice $(E,\tau)$ is said to be: a Lebesgue operator, if $Tx_\alpha\stackrel{\tau}{\to}0$ for every net in $E$ satisfying $x_\alpha\downarrow 0$; a $KB$-operator, if, for every $\tau$-bounded increasing net $x_\alpha$ in $E_+$, there exists an $x\in E$ with $Tx_\alpha\stackrel{\tau}{\to}Tx$; a quasi $KB$-operator, if $T$ takes $\tau$-bounded increasing nets in $E_+$ to $\tau$-Cauchy ones; a Lévi operator, if, for every $\tau$-bounded increasing net $x_\alpha$ in $E_+$, there exists an $x\in E$ such that $Tx_\alpha\stackrel{o}{\to}Tx$; a quasi Levi operator, if $T$ takes $\tau$-bounded increasing nets in $E_+$ to $o$-Cauchy ones. The present article is devoted to the domination problem for the quasi $KB$-operators and the quasi Lévi operators in locally solid vector lattices. Moreover, some properties of Lebesgue operators, Lévi operators, and $KB$-operators are investigated. In particularly, it is proved that the vector space Lebesgue operators is a subalgebra of the algebra of all regular operators.

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