Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Dividing measures and narrow operators

100%

Mykhaylyuk V., Pliev M., Popov M., Sobchuk O.

Studia Mathematica

2015

tom 231

nr 2

97-116

We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far from its original vector lattice structure. Our third main result asserts that every operator such that the density of the range space is less than the density of the domain space, is strictly narrow. This gives a positive answer to Problem 2.17 from "Narrow Operators on Function Spaces and Vector Lattices" by B. Randrianantoanina and the third named author for the case of reals. All the results are obtained for a more general setting of (nonlinear) orthogonally additive operators.

Ograniczanie wyników

1 Studia Mathematica

1 Mykhaylyuk V.

1 Pliev M.

1 Popov M.

1 Sobchuk O.

1 2015

Wyniki wyszukiwania

Dividing measures and narrow operators