Results 1 to 10 of about 37,162 (168)
On Bilinear Narrow Operators [PDF]
Mathematics, 2021 In this article, we introduce a new class of operators on the Cartesian product of vector lattices. We say that a bilinear operator T:E×F→W defined on the Cartesian product of vector lattices E and F and taking values in a vector lattice W is narrow if ...
Marat Pliev +2 more
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G-narrow operators and G-rich subspaces [PDF]
Open Mathematics, 2013 Abstract Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators.
Ivashyna Tetiana
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Points of narrowness and uniformly narrow operators
Karpatsʹkì Matematičnì Publìkacìï, 2017 It is known that the sum of every two narrow operators on $L_1$ is narrow, however the same is false for $L_p$ with $1 < p < \infty$. The present paper continues numerous investigations of the kind.
A.I. Gumenchuk +2 more
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On Narrow Operators from $$L_p$$ into Operator Ideals [PDF]
Mediterranean Journal of Mathematics, 2022 AbstractIt is well known that every $$l_2$$ l 2 -strictly singular operator from $$L_p$$ L p , $$1<p<\infty $$ 1
Jinghao Huang +2 more
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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.
Nariman Magamedovich Abasov
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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.
Marat Pliev, M. M. Popov
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Unconditionally convergent series of operators and narrow operators on $L_1$ [PDF]
Bulletin of the London Mathematical Society, 2003 We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.
Vladimir Kadets +2 more
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$L$-orthogonality in Daugavet centers and narrow operators [PDF]
Journal of Mathematical Analysis and Applications, 2020 We study the presence of $L$-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that, if $\dens(Y)\leq _1$ and $G:X\longrightarrow Y$ is a Daugavet center, then $G(W)$ contains some $L$-orthogonal for every non-empty $w^*$-open subset of $B_{X^{**}}$.
Abraham Rueda Zoca
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Narrow Orthogonally Additive Operators on Lattice-Normed Spaces [PDF]
Siberian Mathematical Journal, 2015 The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between lattice-normed spaces.
Xiao Chun Fang, Marat Pliev
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Narrow operators on lattice-normed spaces [PDF]
Open Mathematics, 2011 Abstract The aim of this article is to extend results of Maslyuchenko, Mykhaylyuk and Popov about narrow operators on vector lattices. We give a new definition of a narrow operator, where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous
Marat Pliev
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