Annals of Functional Analysis

Dominated operators from lattice-normed spaces to sequence Banach lattices

Nariman Abasov, Abd El Monem Megahed, and Marat Pliev

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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|.

Article information

Ann. Funct. Anal., Volume 7, Number 4 (2016), 646-655.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B42: Banach lattices [See also 46A40, 46B40]
Secondary: 47B99: None of the above, but in this section

narrow operators dominated operators lattice-normed spaces Banach lattices


Abasov, Nariman; Megahed, Abd El Monem; Pliev, Marat. Dominated operators from lattice-normed spaces to sequence Banach lattices. Ann. Funct. Anal. 7 (2016), no. 4, 646--655. doi:10.1215/20088752-3660990.

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