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arXiv · 1508.03275

Dominated Operators from a Lattice-Normed Space to a Sequence Banach Lattice

N. Abasov·A. Megahed·M. Pliev
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Abstract

We show that every dominated linear operator from an Banach-Kantorovich space over atomless Dedekind complete vector lattice to a sequence Banach lattice $l_p({\Gamma})$ or $c_0({\Gamma})$ is narrow. As a conse- quence, we obtain that an atomless Banach lattice cannot have a finite dimensional decomposition of a certain kind. Finally we show that if a linear dominated operator T from lattice-normed space V to Banach- Kantorovich space W is order narrow then the same is its exact dominant $\ls T\rs$.

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N. Abasov, A. Megahed, M. Pliev. 2015-08-13. Dominated Operators from a Lattice-Normed Space to a Sequence Banach Lattice. https://doi.org/10.1215/20088752-3660990

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