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Sums of SCD sets and their applications to SCD operators and narrow operators

100%

Kadets V., Shepelska V.

Open Mathematics

2010

tom 8

nr 1

129-134

We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach spaces. An application to narrow operators in spaces with the Daugavet property is given.

Narrow operators on lattice-normed spaces

88%

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

2 Open Mathematics

1 Kadets V.

1 Pliev M.

1 Shepelska V.

1 2011

1 2010

Wyniki wyszukiwania

Sums of SCD sets and their applications to SCD operators and narrow operators

Narrow operators on lattice-normed spaces