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Characterization of Banach Lattices in Terms of Quasi-Interior Points

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  • Egor A. Alekhno

Abstract

In terms of quasi-interior points, criteria that a Banach lattice has order continuous norm or is an -space with a unit are given. For example, if is Dedekind complete and has a weak order unit, then has order continuous norm if and only if the set of quasi-interior points of coincides with the set of weak order units of ; a Banach lattice is an -space with a unit if and only if the set of all quasi-interior points of coincides with the set . Analogous questions are considered for the case of an ordered Banach space with a cone . Moreover, it is shown that every nonzero point of a cone is quasi-interior if and only if . We also study various -properties of a cone ; in particular, the conditions for which the relation with implies that is not a quasi-interior point are considered.

Suggested Citation

  • Egor A. Alekhno, 2013. "Characterization of Banach Lattices in Terms of Quasi-Interior Points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jijmms:507482
    DOI: 10.1155/2013/507482
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