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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
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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

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3. Ellis, H. W., and Snow, D. O., On (L1)* for general measure spaces, Canad. Math. Bull., vol. 6, 1963, 211-229.Google Scholar
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