Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-16T17:13:41.912Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Dual of L1

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis
H. W. Ellis*
Affiliation:
California Institute of Technology and Queen's University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If (X, S,μ) is an arbitrary complemented measure space and X is σ-finite then (L1)* = L∞ or, more precisely, (L1)* is isometric and isomorphic to L∞ by the correspondence

It is well known that there exist non σ-finite spaces with (L1)* ≥ L∞.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 809 - 818
Copyright
Copyright © Canadian Mathematical Society 1965

Footnotes

1)

Partly supported by a National Research Council (Canada) Senior Research Fellowship.

1)

Partly supported by a National Research Council (Canada) Senior Research Fellowship.

References

1. Bourbaki, N., Éléments de Mathématique, Fasc. II, Topologie Générale, Chapters 1,2, 3rd edition, Hermann, Paris, 1961.Google Scholar
2. Bourbaki, N., Eléments de Mathématique, Fasc. XXI, Integration, Chapter 5, Hermann, Paris, 1956.Google Scholar
3. Ellis, H. W., and Snow, D. O., On (L1)* for general measure spaces, Canad. Math. Bull., vol. 6, 1963, 211-229.Google Scholar
4. Halmos, P. R., Measure Theory, Van.Nostrand, New York, 1950.Google Scholar
5. Munroe, M. E., Introduction to Measure and Integration, Addison-Wesley, Cambridge, Mass., 1953.Google Scholar
6. Kakutani, S., Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Annals of Mathematics, 42 (1941), 523-537.Google Scholar
7. Sikorski, R., Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, 1960.Google Scholar