Geodesic
On Orthogonally Additive Operators in Lattice-Normed Spaces
Matematičeskie zametki, Tome 113 (2023) no. 1, pp. 58-74

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In this paper, we study a new class of locally dominated orthogonally additive operators on lattice-normed spaces (LNS). In the first part of the paper, sufficient conditions for the existence of a local exact majorant of a locally dominated operator and formulas for its calculation are given. The second part shows that the $C$-compactness of a dominated orthogonally additive operator acting from a decomposable lattice-normed space to a Banach space with mixed norm implies the $C$-compactness of its exact majorant.
Keywords: orthogonally additive operator, $x$-locally dominated operator, positive operator, $C$-compact operator, lattice-normed space, vector lattice, Banach lattice.
Mots-clés : $x$-local exact majorant 
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N. A. Dzhusoeva; S. Yu. Itarova. On Orthogonally Additive Operators in Lattice-Normed Spaces. Matematičeskie zametki, Tome 113 (2023) no. 1, pp. 58-74. http://geodesic.mathdoc.fr/item/MZM_2023_113_1_a5/