Embeddings of Rearrangement Invariant Spaces that are not Strictly Singular

Embeddings of Rearrangement Invariant Spaces that are not Strictly Singular We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L 1([0,1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L Φ with Φ(x) = exp(x2)-1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Embeddings of Rearrangement Invariant Spaces that are not Strictly Singular

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009825521243
Publisher site
See Article on Publisher Site

Abstract

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L 1([0,1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L Φ with Φ(x) = exp(x2)-1.

Journal

PositivitySpringer Journals

Published: Oct 14, 2004

References

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