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