English

Embeddings of rearrangement invariant spaces that are not strictly singular

Functional Analysis 2009-09-25 v1 Probability

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_Phi with Phi(x) = exp(x^2)-1.

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Cite

@article{arxiv.math/0007058,
  title  = {Embeddings of rearrangement invariant spaces that are not strictly singular},
  author = {S. J. Montgomery-Smith and E. M. Semenov},
  journal= {arXiv preprint arXiv:math/0007058},
  year   = {2009}
}

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Also available at http://www.math.missouri.edu/~stephen/preprints