Equi-bounded on order intervals families of semi-norms
Eduard Emelyanov
TL;DR
This paper proves that families of semi-norms on ordered Banach spaces, which are uniformly bounded on order intervals, are also equi-continuous, linking boundedness and continuity properties.
Contribution
It establishes a new result connecting equi-boundedness on order intervals with equi-continuity for semi-norm families in ordered Banach spaces.
Findings
Families of semi-norms bounded on order intervals are equi-continuous.
The result applies to ordered Banach spaces with closed generating cones.
Provides a theoretical link between boundedness and continuity in this setting.
Abstract
It is proved that equi-bounded on order intervals families of semi-norms on an ordered Banach space with a closed generating cone are equi-continuous.
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Taxonomy
TopicsAdvanced Banach Space Theory · Nonlinear Differential Equations Analysis · Fixed Point Theorems Analysis