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Narrow operators on lattice-normed spaces

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Pliev M.

Open Mathematics

2011

tom 9

nr 6

1276-1287

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 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 so.

Ograniczanie wyników

1 Open Mathematics

1 Pliev M.

1 2011

Wyniki wyszukiwania

Narrow operators on lattice-normed spaces