Hostname: page-component-5c6d5d7d68-sv6ng Total loading time: 0 Render date: 2024-08-18T07:18:19.415Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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)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
(2)Fremlin, D. H.Abstract Köthe spaces. Proc. Cambridge Philos. Soc. 63 (1967) (a) (I) 653–660; (b) (II) 951–956.CrossRefGoogle Scholar
(3)Birkhoff, G.Lattice theory (American Mathematical Society, 1948).Google Scholar
(4)Chacon, R. V. and Krengel, U.Linear modulus of a linear operator. Proc. Amer. Math. Soc. 15 (1964), 553–559.Google Scholar
(5)Krengel, U.Über den Absolutbetrag stetiger linearen Operatoren und seine Anwendung auf ergodische Zerlegungen. Math. Scand. 13 (1963), 151–187.CrossRefGoogle Scholar