Kolmogorof normability theorem turns to be a characterization for the complete normability of a topological vector space by replacing the convexity hypothesis with the sigma convexity one. In particular, the well known theorem that characterizes completeness of a normed vector spaces by means of absolutely convergent series, is obtained as an easy consequence of the Theorem below.

A short remark on Kolmogoroff normability theorem

CARUSO, ANDREA ORAZIO
2002-01-01

Abstract

Kolmogorof normability theorem turns to be a characterization for the complete normability of a topological vector space by replacing the convexity hypothesis with the sigma convexity one. In particular, the well known theorem that characterizes completeness of a normed vector spaces by means of absolutely convergent series, is obtained as an easy consequence of the Theorem below.
2002
Topological vector spaces; Normability criteria; Completeness
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/2917
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