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Minimal decompositions in partially ordered normed vector spaces

Published online by Cambridge University Press:  24 October 2008

A. J. Ellis
A. J. Ellis
Affiliation:
University College of Swansea
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In this paper we study partially ordered vector spaces X whose positive cone K possesses a base which defines a norm in X. A positive decomposition x = y − z of the element x is said to be minimal if ‖x‖ = ‖y‖ + ‖z‖. We proved in (6) that the property that every element of X has a unique minimal decomposition is equivalent to an intersection property for homothetic translates of the base. Section 2 of the present paper analyses this intersection property in much more detail and discusses possible generalizations of it.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 989 - 1000
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

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