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Embeddings of rearrangement invariant spaces that are not strictly singular

S. J. Montgomery-Smith·E. M. Semenov
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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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S. J. Montgomery-Smith, E. M. Semenov. 2000-07-10. Embeddings of rearrangement invariant spaces that are not strictly singular. https://arxiv.org/abs/math/0007058

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