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arXiv:math/0007058 [math.FA]AbstractReferencesReviewsResources

Embeddings of rearrangement invariant spaces that are not strictly singular

S. J. Montgomery-Smith, E. M. Semenov

Published 2000-07-10Version 1

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.

Comments: Also available at http://www.math.missouri.edu/~stephen/preprints
Journal: Positivity, 4, (2000), 397-404.
Categories: math.FA, math.PR
Subjects: 46E30, 47B38, 60G50
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