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Banach Limits Revisited
Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Faculty of Mathematics and Computer Science, Fern Universität Hagen, Hagen, Germany
- 1 Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- 2 Faculty of Mathematics and Computer Science, Fern Universität Hagen, Hagen, Germany
Advances in Pure Mathematics·Volume 06 (2016)·Pages 1022–1036·Published 12 December 2016·DOI10.4236/apm.2016.613075
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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.
KeywordsOrder Unit Normed SpacesBase Normed SpacesBanach Limits
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