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A constructive approach to the duality theorem for certain Orlicz spaces

Published online by Cambridge University Press:  24 October 2008

D. L. Johns  and
C. G. Gibson
D. L. Johns
Affiliation:
University of Liverpool
C. G. Gibson
Affiliation:
University of Liverpool
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Extract

One of the intriguing complications of constructive analysis is that it does not seem possible to obtain examples of inseparable Banach spaces; more precisely, when one comes to study explicit examples one finds that one cannot assign a constructively denned norm to every vector in the space. One of the objectives of (2) was to make a detailed study of an explicit class of Banach spaces, containing both separable and inseparable examples, in the hope that one might begin better to understand these matters. We chose for this study the class of Orlicz spaces, primarily because the simplest examples (namely the Lebesgue spaces LP) had already been the objective of detailed constructive work in (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 49 - 69
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

(1)Bishop, E.Foundations of Constructive Analysis. McGraw-Hill, 1967.Google Scholar
(2)Johns, D. L. A Constructive Approach to Duality and Orlicz Spaces. Thesis, University of Liverpool, 1977.Google Scholar
(3)Krasnosel'Skii, M. A. And Rutickii, Y. B.Convex Functions and Orlicz Spaces. North Holland, 1961.Google Scholar
(4)Luxemburg, W. A. J. Banach Function Spaces. Thesis, Technische Hogeschool te Delft, 1955.Google Scholar
(5)Zaanen, A. C.Linear Analysis. North Holland, 1953.Google Scholar