Results 11 to 20 of about 332,343 (256)
Narrow operators and the Daugavet property for ultraproducts [PDF]
Positivity, 2005 We show that if $T$ is a narrow operator on $X=X_{1}\oplus_{1} X_{2}$ or $X=X_{1}\oplus_{\infty} X_{2}$, then the restrictions to $X_{1}$ and $X_{2}$ are narrow and conversely. We also characterise by a version of the Daugavet property for positive operators on Banach lattices which unconditional sums of Banach spaces inherit the Daugavet property, and
Dmitriy Bilik +7 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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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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Narrow operators on lattice-normed spaces [PDF]
Open Mathematics, 2013 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 narrow and C-compact operators
Владикавказский математический журнал, 2018 В работе рассматриваются узкие линейные операторы, заданные на пространстве Банаха - Канторовича и принимающие значение в банаховом пространстве. Установлено, что сумма двух операторов S+T, где S - узкий оператор, а T- (bo)-непрерывный C-компактный оператор, также является узким оператором.
Nariman Abasov, Marat Pliev
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On Enflo and narrow operators acting on $L_p$ [PDF]
, 2012 The first part of the paper is inspired by a theorem of H. Rosenthal, that if an operator on $L_1[0,1]$ satisfies the assumption that for each measurable set $A \subseteq [0,1]$ the restriction $T \bigl|_{L_1(A)}$ is not an isomorphic embedding, then the operator is narrow.
Volodymyr Mykhaylyuk +2 more
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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.
Vladimir Kadets, Varvara Shepelska
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On sign embeddings and narrow operators on $L_2$ [PDF]
, 2016 The goal of this note is two-fold. First we present a brief overview of "weak" embeddings, with a special emphasis on sign embeddings which were introduced by H. P. Rosenthal in the early 1980s. We also discuss the related notion of narrow operators, which was introduced by A. Plichko and M. Popov in 1990.
Beata Randrianantoanina
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On sums of narrow and compact operators
Positivity, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
O. Fotiy +3 more
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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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