We introduce and study the metric or extreme versions of the notions of a flat and an injective normed module. The relevant definitions, in contrast with the standard known ones, take into account the exact value of the norm of the module. The main result gives a full characterization of extremely flat objects within a certain category of normed modules. As a corollary, some Hahn-Banach type theorems for normed modules are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-2-3,
author = {A. Ya. Helemskii},
title = {Metric version of flatness and Hahn-Banach type theorems for normed modules over sequence algebras},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {135-160},
zbl = {1241.46025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-2-3}
}
A. Ya. Helemskii. Metric version of flatness and Hahn-Banach type theorems for normed modules over sequence algebras. Studia Mathematica, Tome 204 (2011) pp. 135-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-2-3/