Embeddings of rearrangement invariant spaces that are not strictly singular

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