Open Access
November 2016 Dominated operators from lattice-normed spaces to sequence Banach lattices
Nariman Abasov, Abd El Monem Megahed, Marat Pliev
Ann. Funct. Anal. 7(4): 646-655 (November 2016). DOI: 10.1215/20088752-3660990


We show that every dominated linear operator from a Banach–Kantorovich space over an atomless Dedekind-complete vector lattice to a sequence Banach lattice p(Γ) or c0(Γ) is narrow. As a consequence, we obtain that an atomless Banach lattice cannot have a finite-dimensional decomposition of a certain kind. Finally, we show that the order-narrowness of a linear dominated operator T from a lattice-normed space V to the Banach space with a mixed norm (W,F) over an order-continuous Banach lattice F implies the order-narrowness of its exact dominant |T|.


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Nariman Abasov. Abd El Monem Megahed. Marat Pliev. "Dominated operators from lattice-normed spaces to sequence Banach lattices." Ann. Funct. Anal. 7 (4) 646 - 655, November 2016.


Received: 8 November 2015; Accepted: 11 May 2016; Published: November 2016
First available in Project Euclid: 5 October 2016

zbMATH: 1365.46018
MathSciNet: MR3555756
Digital Object Identifier: 10.1215/20088752-3660990

Primary: 46B42
Secondary: 47B99

Keywords: Banach lattices , dominated operators , lattice-normed spaces , narrow operators

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.7 • No. 4 • November 2016
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