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A note on symmetric basic sequences in Lp(Lq)

Published online by Cambridge University Press:  24 October 2008

Yves Raynaud
Yves Raynaud
Affiliation:
Equipe d'Analyse (CNRS), Université Paris-6, 4, place Jussieu, 75252-PARIS-Cedex 05, France
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Extract

Subspaces of Lp spanned by symmetric independent identically distributed random variables were identified as Orlicz spaces by Bretagnolle and Dacunha-Castelle[1], who showed that, conversely, in the case p ≤ 2, every p-convex, 2-concave Orlicz space is isomorphic to a subspace of Lp. This was extended by Dacunha-Castelle [3] to subspaces of Lp with symmetric basis, which appear as ‘p-means’ of Orlicz spaces (see [9] for the corresponding finite-dimensional result, and [12] for the case of rearrangement invariant function spaces). On the contrary the only subspaces with symmetric basis of Lp for p ≥ 2 are lp and l2 (if one does not care about isomorphy constants).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 183 - 194
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

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