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On Orthogonally Additive Operators in Lattice-Normed Spaces

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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.

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Funding

This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. \(075-02-2021-1552\).)

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Authors and Affiliations

  1. North Ossetian State University, Vladikavkaz, 362025, Russia

    N. A. Dzhusoeva & S. Yu. Itarova

Authors
  1. N. A. Dzhusoeva
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  2. S. Yu. Itarova
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Corresponding author

Correspondence to N. A. Dzhusoeva.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 58–74 https://doi.org/10.4213/mzm13613.

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Dzhusoeva, N.A., Itarova, S.Y. On Orthogonally Additive Operators in Lattice-Normed Spaces. Math Notes 113, 59–71 (2023). https://doi.org/10.1134/S0001434623010078

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  • DOI: https://doi.org/10.1134/S0001434623010078

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