This article is cited in 8 papers

On Orthogonally Additive Operators in Lattice-Normed Spaces

N. A. Dzhusoeva, S. Yu. Itarova

North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz

Abstract: 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, $x$-local exact majorant, positive operator, $C$-compact operator, lattice-normed space, vector lattice, Banach lattice.

UDC: 517

Received: 05.06.2022
Revised: 06.08.2022

DOI: 10.4213/mzm13613

 English version: Mathematical Notes, 2023, 113:1, 59–71

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