Narrow operators on lattice-normed spaces

• Autorzy: Marat Pliev
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Narrow operators; GAM-compact operators; Dominated operators; Lattice-normed spaces; Banach lattices

Kategorie tematyczne

• 46B99: None of the above, but in this section
• 47B99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1276-1287

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Marat Pliev

• South Mathematical Institute of the Russian Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0090-3