Dedekind complete and order continuous Banach $C(K)$-modules
Functional Analysis
2018-12-13 v1
Abstract
We extend the notions of Dedekind complete and sigma-Dedekind complete Banach lattices to Banach C(K)-modules. As our main result we prove for these modules an analogue of Lozanovsky's well known characterization of Banach lattices with order continuous norm.
Cite
@article{arxiv.1812.05025,
title = {Dedekind complete and order continuous Banach $C(K)$-modules},
author = {Arkady Kitover and Mehmet Orhon},
journal= {arXiv preprint arXiv:1812.05025},
year = {2018}
}