[Banach] Abstract of a paper by Abasov, N., Megaled, A., and Pliev, M

This is an announcement for the paper "Dominated oprerators from a lattice-normed space to a sequence Banach lattice" by Abasov,N., Megaled,A., and Pliev,M.

Abstract: 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 $\ls T\rs$.

Archive classification: math.FA

Mathematics Subject Classification: 47H30, 46B42

Submitted from: martin.weber@tu-dresden.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.03275

or

http://arXiv.org/abs/1508.03275