Embeddings of rearrangement invariant spaces that are not strictly singular

被引：7

作者：

Montgomery-Smith, SJ ^{[1
]}

Semenov, EM

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Voronezh State Univ, Dept Math, Voronezh 394693, Russia

来源：

POSITIVITY | 2000年 / 4卷 / 04期

关键词：

rearrangement invariant space; strictly singular mapping; Rademacher function; Orlicz space;

D O I：

10.1023/A:1009825521243

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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>(*) over bar * (x) = exp(x(2))-1.

引用

页码：397 / 402

页数：6

共 50 条

[41] REARRANGEMENT INVARIANT KOTHE SPACES
SILVERMAN, G
MATHEMATISCHE ANNALEN, 1970, 189 (03) : 222 - +
[42] Bases of rearrangement invariant spaces
K. S. Kazarian
E. M. Semenov
S. N. Uksusov
Russian Mathematics, 2008, 52 (5) : 41 - 46
[43] On the essential norm of the Cauchy singular integral operator in weighted rearrangement-invariant spaces
Karlovich, AY
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2000, 38 (01) : 28 - 50
[44] Singular integral operators with piecewise continuous coefficients in reflexive rearrangement-invariant spaces
Karlovich, AY
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1998, 32 (04) : 436 - 481
[45] On the essential norm of the Cauchy singular integral operator in weighted rearrangement-invariant spaces
Alexei Yu. Karlovich
Integral Equations and Operator Theory, 2000, 38 : 28 - 50
[46] Singular integral operators with piecewise continuous coefficients in reflexive rearrangement-invariant spaces
Alexei Yu. Karlovich
Integral Equations and Operator Theory, 1998, 32 : 436 - 481
[47] STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS ON TOPOLOGICAL VECTOR-SPACES
SHANNON, GP
PROCEEDINGS OF THE ROYAL IRISH ACADEMY SECTION A-MATHEMATICAL AND PHYSICAL SCIENCES, 1973, 73 (22) : 303 - 308
[48] STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS ON SPACES OF CONTINUOUS-FUNCTIONS
ABBOTT, C
BATOR, E
LEWIS, P
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1991, 110 : 505 - 521
[49] COMPACT AND STRICTLY SINGULAR OPERATORS ON ORLICZ SPACES
KALTON, NJ
ISRAEL JOURNAL OF MATHEMATICS, 1977, 26 (02) : 126 - 136
[50] Disjointly strictly singular inclusions of symmetric spaces
S. V. Astashkin
Mathematical Notes, 1999, 65 : 3 - 12

← 1 2 3 4 5 →