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

• Autorzy: A. Ya. Helemskii
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 206
• Numer: 2
• Strony: 135-160

Daty

wydano

2011

Twórcy

autor

A. Ya. Helemskii

• Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia

Identyfikatory

DOI

10.4064/sm206-2-3