Narrow orthogonally additive operators in lattice-normed spaces

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. © 2017, Pleiades Publishing, Ltd.

Authors
Pliev M.A. 1, 2 , Fang X.3
Number of issue
1
Language
English
Pages
134-141
Status
Published
Volume
58
Year
2017
Organizations
  • 1 Southern Mathematical Institute, Vladikavkaz, Russian Federation
  • 2 Peoples’ Friendship University of Russia, Moscow, Russian Federation
  • 3 Tongji University, Shanghai, China
Keywords
Banach lattice; dominated Urysohn operator; lattice-normed space; narrow operator; orthogonally additive operator; vector lattice
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6257/
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