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Abstract Köthe spaces. III

Published online by Cambridge University Press:  24 October 2008

D. H. Fremlin
D. H. Fremlin
Affiliation:
United College, Chinese University of Hong Kong
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Extract

In this paper I shall be considering the space of linear maps between two (perfect) Riesz spaces, and shall show how certain topological properties of these maps are related to the natural order structure of the space. The fundamental result is (e) of section 4, certain special cases of which have been treated in (4) and (5), using a less elliptic method of proof. Probably the most interesting new result in the present paper is section 10 in the special case of both L and M× being L1 spaces (so that |σ| (L, L×) and |σ| (M×, M) are the norm topologies ((2 b), section 7) and Λ(L; M×) is the space of norm-continuous linear maps).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 957 - 962
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Luxemburg, W. A. J. and Zaanen, A. C.Notes on Banach function spaces. Nederl. Akad. Wetensch Proc. Ser. A. (a) (Note VI) 66 (1963), 655–668; (b) (Note VII) 67 (1964), 104–119.CrossRefGoogle Scholar
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