Metric version of flatness and Hahn–Banach type theorems for normed modules over sequence algebras

Tom 206 / 2011

A. Ya. Helemskii Studia Mathematica 206 (2011), 135-160 MSC: Primary 46H25. DOI: 10.4064/sm206-2-3


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.


  • A. Ya. HelemskiiFaculty of Mechanics and Mathematics
    Moscow State University
    Moscow 119992, Russia

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