Results 1 to 10 of about 269 (104)
On linear sections of orthogonally additive operators
Математичні Студії, 2022 Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that,
A. Gumenchuk, I. Krasikova, M. Popov
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Lateral continuity and orthogonally additive operators
Karpatsʹkì Matematičnì Publìkacìï, 2015 We generalize the notion of a laterally convergent net from increasing nets to general ones and study the corresponding lateral continuity of maps. The main result asserts that, the lateral continuity of an orthogonally additive operator is equivalent to
A.I. Gumenchuk
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On the Sum of Narrow Orthogonally Additive Operators
Russian Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly +3 more sources
Results in Mathematics, 2022 AbstractGiven a Riesz space E and $$0 < e \in E$$ 0 < e ∈ E , we introduce and study an order continuous orthogonally additive operator which is an $$\varepsilon $$ ε
Mikhail Popov, Volodymyr Mykhaylyuk
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On Compact Orthogonally Additive Operators [PDF]
Lobachevskii Journal of Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Basaeva, Elena +2 more
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Disjointness-preserving orthogonally additive operators in vector lattices
Banach Journal of Mathematical Analysis, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marat Pliev, Nariman Abasov
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On orthogonally additive band operators and orthogonally additive disjointness preserving operators
Turkish Journal of Mathematics, 2023 Let $M$ and $N$ be Archimedean vector lattices. We introduce orthogonally additive band operators and orthogonally additive inverse band operators from $M$ to $N$ and examine their properties. We investigate the relationship between orthogonally additive band operators and orthogonally additive disjointness preserving operators and show that under some
TURAN, BAHRİ, Tulu, Demet
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Orthogonally Biadditive Operators
Journal of Function Spaces, 2021 In this article, we introduce and study a new class of operators defined on a Cartesian product of ideal spaces of measurable functions. We use the general approach of the theory of vector lattices.
Nonna Dzhusoeva +2 more
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Projection lateral bands and lateral retracts
Karpatsʹkì Matematičnì Publìkacìï, 2020 A projection lateral band $G$ in a Riesz space $E$ is defined to be a lateral band which is the image of an orthogonally additive projection $Q: E \to E$ possessing the property that $Q(x)$ is a fragment of $x$ for all $x \in E$, called a lateral ...
A. Kamińska, I. Krasikova, M. Popov
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Narrow orthogonally additive operators [PDF]
Positivity, 2013 We extend the notion of narrow operators to nonlinear maps on vector lattices. The main objects are orthogonally additive operators and, in particular, abstract Uryson operators. Most of the results extend known theorems obtained by O. Maslyuchenko, V. Mykhaylyuk and the second named author published in Positivity 13 (2009), pp.
Pliev, Marat, Popov, Mikhail
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