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

中图分类号：

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.

引用

页码：397 / 402

页数：5

共 6 条

[1]

Kalton N.J.(1984)Representations of Operators between Function Spaces Indiana U. Math. J. 33 639-665

[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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