TITLE:
Banach Limits Revisited
AUTHORS:
Diethard Pallaschke, Dieter Pumplün
KEYWORDS:
Order Unit Normed Spaces, Base Normed Spaces, Banach Limits
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.13,
December
23,
2016
ABSTRACT: Order unit normed linear spaces are a special type of regularly ordered normed linear spaces and therefore the first section is a short collection of the fundamental results on this type of normed linear spaces. The connection between order unit normed linear spaces and base normed linear spaces within the category of regularly ordered normed linear spaces is described in Section 2, and Section 3 at last, contains the results on Banach limits in an arbitrary order unit normed linear space. It is shown that the original results on Banach limits are valid for a greater range.