Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 4 (2016), 646-655.
Dominated operators from lattice-normed spaces to sequence Banach lattices
We show that every dominated linear operator from a Banach–Kantorovich space over an atomless Dedekind-complete vector lattice to a sequence Banach lattice or 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 from a lattice-normed space to the Banach space with a mixed norm over an order-continuous Banach lattice implies the order-narrowness of its exact dominant ||.
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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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. https://projecteuclid.org/euclid.afa/1475685111