Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T23:28:48.831Z Has data issue: false hasContentIssue false

Abstract Köthe spaces. IV

Published online by Cambridge University Press:  24 October 2008

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

Extract

In this paper I investigate the completed projective tensor product of two perfect Riesz spaces, and show how a natural order structure on this renders it also a perfect Riesz space. Sections 7–14 contain interesting order-topological properties of this tensor product. Finally, section 15 describes how the tensor product of function spaces may be represented as a function space, in the manner of (1 b).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Fremlin, D. H.Abstract Köthe spaces. Proc. Cambridge Philos. Soc. (a) I; (b) II; (c) III.Google Scholar
(2)Luxemburg, W. A. J. and Zaanen, A. C.Notes on Banach function spaces. Nederl. Akad. Wetensch. Proc. Ser. A. (a) (Note VI) 66 (1963), 655668. (b) (Note VIII) 67 (1964), 104–119.CrossRefGoogle Scholar
(3)Schwartz, L.Produits tensoriels topologiques, etc. (Seminar notes, mimeographed.) Secrétariat mathématique (Paris, 1954).Google Scholar
(4)Grothendieck, A.Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. 16 (1955).Google Scholar
(5)Nakano, H.Product spaces of semi-ordered linear spaces. J. Fac. Sci. Hokkaido University 12 (1953), 163240; reprinted in Semi-ordered linear spaces (Tokyo, 1955; distributed by Maruzen).Google Scholar