# Narrow operators on lattice-normed spaces

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1276-1287
- ISSN: 2391-5455

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topMarat Pliev. "Narrow operators on lattice-normed spaces." Open Mathematics 9.6 (2011): 1276-1287. <http://eudml.org/doc/269204>.

@article{MaratPliev2011,

abstract = {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.},

author = {Marat Pliev},

journal = {Open Mathematics},

keywords = {Narrow operators; GAM-compact operators; Dominated operators; Lattice-normed spaces; Banach lattices; narrow operators; dominated operators; lattice-normed spaces},

language = {eng},

number = {6},

pages = {1276-1287},

title = {Narrow operators on lattice-normed spaces},

url = {http://eudml.org/doc/269204},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Marat Pliev

TI - Narrow operators on lattice-normed spaces

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1276

EP - 1287

AB - 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.

LA - eng

KW - Narrow operators; GAM-compact operators; Dominated operators; Lattice-normed spaces; Banach lattices; narrow operators; dominated operators; lattice-normed spaces

UR - http://eudml.org/doc/269204

ER -

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