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Narrow operators on lattice-normed spaces

100%

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.

Characterization of intermediate values of the triangle inequality II

76%

Sano H., Izumida T., Mitani K.-I., Ohwada T., Saito K.-S.

Open Mathematics

2014

tom 12

nr 5

778-786

In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.

Ograniczanie wyników

2 Open Mathematics

1 Izumida T.

1 Mitani K.-I.

1 Ohwada T.

1 Pliev M.

1 Saito K.-S.

1 Sano H.

1 2014

1 2011

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Narrow operators on lattice-normed spaces

Characterization of intermediate values of the triangle inequality II