Results 1 to 10 of about 362,488 (307)
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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Some problems on narrow operators on function spaces [PDF]
Open Mathematics, 2014 Abstract It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow ...
Popov Mikhail +2 more
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Domination Problem for Narrow Orthogonally Additive Operators [PDF]
Positivity, 2015 12 pages. arXiv admin note: text overlap with arXiv:1309.6074.
Marat Pliev
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UNCONDITIONALLY CONVERGENT SERIES OF OPERATORS AND NARROW OPERATORS ON $L_1$ [PDF]
Bulletin of the London Mathematical Society, 2005 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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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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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 K the $F$-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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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. В. Попов
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Narrow operators on vector-valued sup-normed spaces [PDF]
Illinois Journal of Mathematics, 2002 19 ...
Dmitriy Bilik +4 more
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