Embeddings of Rearrangement Invariant Spaces that are not Strictly Singular |
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| Authors: | Montgomery-Smith S J Semenov E M |
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| Institution: | (1) Department of Mathematics, University of Missouri, Columbia, MO, 65211, U.S.A.;(2) Department of Mathematics, Voronezh State University, Universitetskaya pl.1, Voronezh, 394693, Russia |
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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
 with (x) = exp(x2)-1. |
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| Keywords: | rearrangement invariant space strictly singular mapping Rademacher function Orlicz space |
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