Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T02:34:01.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable subspaces of L1 + L∞

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

1. In this paper, I apply the results of (4) to a class of function spaces distinguished by their invariance under a certain family of operators. This class contains the Lp spaces (indeed, all Orlicz spaces) and the symmetric Köthe spaces of (5). My original objective was simply a more general expression of the ideas of (5), but I found myself taking up a rather different approach.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 625 - 644
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)Chacon, R. V. and Krengel, U.Linear modulus of a linear operator. Proc. Amer. Math. Soc. 15 (1964), 553–559.Google Scholar
(2)Dieudonné, J.Sur les Espaces de Köthe. J. Analyse Math. 1 (1951), 81–115.CrossRefGoogle Scholar
(3)Dunford, N. and Schwartz, J. T.Linear operators, part I (Interscienoe, New York, 1958).Google Scholar
(4)Fremlin, D. H.Abstract Köthe Spaces. Proc. Cambridge Philos. Soc. (4a), I; (4b), II; (4c), III.Google Scholar
(5)Garling, D. J. H.On symmetric sequence spaces. Proc. London Math. Soc. 16 (1966), 85–106.CrossRefGoogle Scholar
(6)Hardy, G. H., Littlewood, J. E. and Pólya, G.Inequalities (Cambridge University Press, 1934).Google Scholar
(7)Luxemburg, W. A. J. and Zaanen, A. C.Notes on Banach function spaces. Nederl. Akad. Wetensch. Ser. A. (7d) Note IV 66 (A), 251–263; (7h) Note VIII 67 (A), 104–119.CrossRefGoogle Scholar
(8)Luxemburg, W. A. J. and Zaanen, A. C.Some examples of normed Köthe spaces. Math. Ann. 162 (1966), 337–350.CrossRefGoogle Scholar
(9)O'Neil, R. and Weiss, G.The Hilbert transform and rearrangement of functions. Studio, Math. 23 (1963), 189–198.CrossRefGoogle Scholar
(10)Zaanen, A. C.Linear analysis (P. Noordhoff, Groningen, 1953).Google Scholar
(11)Bourbaki, N.Espaces Vectoriels Topologiques. (Hermann, Paris, 1955; Actualités Scientifiques et Industrielles § 1220).Google Scholar