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Winter 2019 Dominated orthogonally additive operators in lattice-normed spaces
Nariman Abasov, Marat Pliev
Adv. Oper. Theory 4(1): 251-264 (Winter 2019). DOI: 10.15352/aot.1804-1354

Abstract

‎In this paper, we introduce a new class of operators in lattice-normed spaces‎. ‎We say that an orthogonally additive operator $T$ from a lattice-normed space $(V,E)$ to a lattice-normed space‎ ‎$(W,F)$ is dominated‎, ‎if there exists a positive orthogonally additive operator $S$ from $E$ to $F$ such that $\vert Tx \vert \leq S \vert x \vert$ for any element $x$ of $(V,E)$‎. ‎We show that under some mild‎ ‎conditions‎, ‎a dominated orthogonally additive operator has an exact dominant and obtain formulas for calculating the exact dominant of a dominated orthogonally additive operator‎. ‎In the last part of the‎ ‎paper we consider laterally-to-order continuous operators‎. ‎We prove that a dominated orthogonally additive operator is laterally-to-order continuous if and only if the same is its exact dominant‎.

Citation

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Nariman Abasov. Marat Pliev. "Dominated orthogonally additive operators in lattice-normed spaces." Adv. Oper. Theory 4 (1) 251 - 264, Winter 2019. https://doi.org/10.15352/aot.1804-1354

Information

Received: 27 April 2018; Accepted: 2 August 2018; Published: Winter 2019
First available in Project Euclid: 20 September 2018

zbMATH: 06946453
MathSciNet: MR3867344
Digital Object Identifier: 10.15352/aot.1804-1354

Subjects:
Primary: 47H30
Secondary: 47H99

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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