Order norm completions of cone metric spaces
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Date
2011
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Publisher
Taylor & Francis inc
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Abstract
In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.
Description
Abdeljawad, Thabet/0000-0002-8889-3768
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Keywords
Absolute Value Property, Cone Banach, Cone Isometry, Cone Metric, Strongly Minihedral, Uniformly Continuous
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Citation
Abdeljawad, T. (2011). Order norm completions of cone metric spaces. Numerical Functional Analysis and Optimization, 32(5), 477-495. http://dx.doi.org/10.1080/01630563.2011.563892
WoS Q
Q3
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Q3
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Volume
32
Issue
5
Start Page
477
End Page
495