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arXiv · 1309.5490

Narrow operators on lattice-normed spaces

M. Pliev
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Abstract

The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. 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 linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator is narrow if and only if its exact dominant is narrow.

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M. Pliev. 2013-09-21. Narrow operators on lattice-normed spaces. https://arxiv.org/abs/1309.5490

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