This article is cited in 4 scientific papers (total in 4 papers)
Narrow orthogonally additive operators in lattice-normed spaces
M. A. Plievab, X. Fangc
a Southern Mathematical Institute, Vladikavkaz, Russia
b Peoples' Friendship University of Russia, Moscow, Russia
c Department of Mathematics, Tongji University, Shanghai, China
We consider a new class of narrow orthogonally additive operators in lattice-normed spaces and prove the narrowness of every $C$-compact norm-laterally-continuous orthogonally additive operator from a Banach–Kantorovich space $V$ into a Banach space $Y$. Furthermore, every dominated Urysohn operator from $V$ into a Banach sequence lattice $Y$ is also narrow. We establish that the order narrowness of a dominated Urysohn operator from a Banach–Kantorovich space $V$ into a Banach space with mixed norm $W$ implies the order narrowness of the least dominant of the operator.
vector lattice, Banach lattice, lattice-normed space, orthogonally additive operator, dominated Urysohn operator, narrow operator.
|Russian Foundation for Basic Research
|The first author was supported by the Russian Foundation for Basic Research (Grant 15-51-53119) and by
the Ministry of Education and Science of the Russian Federation (Agreement 02.a03.21.0008 of 24 June 2016). The
second author was supported by the National Natural Science Foundation of China (Grant 11511130012).
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Siberian Mathematical Journal, 2017, 58:1, 134–141
M. A. Pliev, X. Fang, “Narrow orthogonally additive operators in lattice-normed spaces”, Sibirsk. Mat. Zh., 58:1 (2017), 174–184; Siberian Math. J., 58:1 (2017), 134–141
Citation in format AMSBIB
\by M.~A.~Pliev, X.~Fang
\paper Narrow orthogonally additive operators in lattice-normed spaces
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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