On separate order continuity of orthogonally additive operators

Krasikova Iryna Volodymyrivna; Pliev M. A.; Popov Mykhailo Mykhailovych; Fotiy Olena Georgiivna

doi:https://doi.org/10.31861/bmj2021.01.17

Krasikova Iryna Volodymyrivna ¹ , Pliev M. A. ² , Popov Mykhailo Mykhailovych ^3,4 , Fotiy Olena Georgiivna ⁴

¹ Department of Fundamental and Applied Mathematics, Zaporizhzhya National University, Zaporizhzhia region, Zaporizhzhya, 69061, Ukraine

² Southern Mathematical Institute of the Russian Academy of Sciences, R, 0, R

³ Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, 76000, Ukraine

⁴ Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

DOI: https://doi.org/10.31861/bmj2021.01.17

Keywords: vector lattice, Riesz space, orthogonally additive operator, order continuous operator

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Abstract

Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping $f : E → F$ between vector lattices $E$ and $F$ is horizontally-to-order continuous provided $f$ sends laterally increasing order convergent nets in $E$ to order convergent nets in $F$, and $f$ is uniformly-to-order continuous provide $f$ sends uniformly convergent nets to order convergent nets).

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ACS Style: Krasikova, I.V.; Pliev, M.A.; Popov, M.M.; Fotiy, O.G. On separate order continuity of orthogonally additive operators. Bukovinian Mathematical Journal. 2021, 9 https://doi.org/https://doi.org/10.31861/bmj2021.01.17
AMA Style: Krasikova IV, Pliev MA, Popov MM, Fotiy OG. On separate order continuity of orthogonally additive operators. Bukovinian Mathematical Journal. 2021; 9(1). https://doi.org/https://doi.org/10.31861/bmj2021.01.17
Chicago/Turabian Style: Iryna Volodymyrivna Krasikova, M. A. Pliev, Mykhailo Mykhailovych Popov, Olena Georgiivna Fotiy. 2021. "On separate order continuity of orthogonally additive operators". Bukovinian Mathematical Journal. 9 no. 1. https://doi.org/https://doi.org/10.31861/bmj2021.01.17

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