This article is cited in 20 papers

Narrow orthogonally additive operators in lattice-normed spaces

M. A. Pliev^ab, X. Fang<sup>c

a</sup> Southern Mathematical Institute, Vladikavkaz, Russia
^b Peoples' Friendship University of Russia, Moscow, Russia
^c Department of Mathematics, Tongji University, Shanghai, China

Abstract: 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.

Keywords: vector lattice, Banach lattice, lattice-normed space, orthogonally additive operator, dominated Urysohn operator, narrow operator.

UDC: 517.98+519.46

MSC: 35R30

Received: 25.01.2016

DOI: 10.17377/smzh.2017.58.117

 English version: Siberian Mathematical Journal, 2017, 58:1, 134–141

Bibliographic databases:

• 
• 
• 
•