Embeddings of Rearrangement Invariant Spaces that are not Strictly Singular

被引：0
作者：
S. J. Montgomery-Smith
E. M. Semenov
机构：
[1] University of Missouri,Department of Mathematics
[2] Voronezh State University,Department of Mathematics
来源：
Positivity | 2000年 / 4卷
关键词：
rearrangement invariant space; strictly singular mapping; Rademacher function; Orlicz space;
D O I：
暂无
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学科分类号：
摘要：
We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1([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 LΦ with Φ(x) = exp(x2)-1.
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页码：397 / 402
页数：5
相关论文
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  • [2] Montgomery-Smith S.J.(1998)Random rearrangements and operators 25 Years of Voronezh Winter Mathematical School, Proceedings in honor of 80th birthday of S. Krein 184 157-183
  • [3] Semenov E.M.(1997)Rademacher series in symmetric spaces Singularities of the embedding operator for symmetric function spaces on [0, 1] 62 549-563
  • [4] Novikov S.J.(1975)undefined Anal. Math. 1 207-222
  • [5] Rodin S.J.(undefined)undefined undefined undefined undefined-undefined
  • [6] Semenov E.M.(undefined)undefined undefined undefined undefined-undefined
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