Hahn-Banach type theorems for hypolinear functionals on preordered topological vector spaces

Bernd Anger and Jörn Lembcke

Vol. 54 (1974), No. 1, 13–33

DOI: 10.2140/pjm.1974.54.13

Abstract

This article deals with existence and extension theorems for continuous positive linear forms, dominated by hypolinear functionals, i.e., sublinear functionals which may attain the value +∞.

It is proved that a hypolinear functional dominates a continuous positive linear form if and only if its largest increasing and hypolinear minorant exists and is lower semicontinuous at the origin. Conditions are given which imply that any increasing hypolinear functional is lower semicontinuous at the origin.

Mathematical Subject Classification 2000

Primary: 46A40

Milestones

Received: 26 April 1973

Published: 1 September 1974