Embeddings of rearrangement invariant spaces that are not strictly singular

Details Embeddings of rearrangement invariant spaces that are not strictly singular Embeddings of rearrangement invariant spaces that are not strictly singular

2000-07-10

arxiv.org/abs/math/0007058v1

Positivity, 4, (2000), 397-404.

Mathematics

Functional Analysis

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

Scientific paper

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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