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Order norm completions of cone metric spaces

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Date

2011

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Taylor & Francis inc

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Matematik
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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

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

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Q3

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Volume

32

Issue

5

Start Page

477

End Page

495