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A note on simplex spaces

Published online by Cambridge University Press:  24 October 2008

Kung-Fu Ng
Kung-Fu Ng
Affiliation:
United College, Chinese University of Hong Kong
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Extract

Let X be a real Banach space which is partially ordered by a closed cone C. Let X* denote the Banach dual space, and let

X is called a simplex space (2) if (X*, C*,‖·‖) is an AL-space. We proved in (3) that X is a simplex space if and only if X is an approximate order-unit-normed space and has the Riesz decomposition property. When the given norm on X is an order-unit norm, some representation theorems are obtained by Effros ((2), theorem 4·8) and Sterrmer ((6), theorem 4·3). In this note, we shall study the representation problem for more general simplex spaces. One of our aims is to prove that X is equivalent to C0(ω) if and only if X has the Urysohn property (for definitions, see below).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 559 - 562
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

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