Results 1 to 10 of about 23,562 (146)
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
Pliev Marat
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G-narrow operators and G-rich subspaces
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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Sums of SCD sets and their applications to SCD operators and narrow operators
Open Mathematics, 2010 Abstract We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach spaces. An application to narrow operators in spaces with the Daugavet property is given.
Kadets Vladimir, Shepelska Varvara
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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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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
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
Marat Pliev +2 more
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L-orthogonality in Daugavet centers and narrow operators
Journal of Mathematical Analysis and Applications, 2022 We study the presence of $L$-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that, if $\dens(Y)\leq ω_1$ 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 [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, Mikhail Popov
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Domination problem for narrow orthogonally additive operators [PDF]
Positivity, 2016 12 pages. arXiv admin note: text overlap with arXiv:1309.6074.
Marat Pliev
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On the sum of a narrow and a compact operators
Journal of Functional Analysis, 2014 Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every Köthe $F$-space $X$ and for every locally convex $F$-space $Y$ the sum $T_1+T_2$ of a narrow operator $T_1:X\to Y$ and a compact narrow operator $T_2:X\to Y$ is a narrow ...
Volodymyr Mykhaylyuk
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