The Banach-Saks property in rearrangement invariant spaces

被引：28

作者：

Dodds, PG ^{[1
]}

Semenov, EM

Sukochev, FA

机构：

[1] Flinders Univ S Australia, Sch Informat & Engn, Bedford Pk, SA 5042, Australia

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

来源：

STUDIA MATHEMATICA | 2004年 / 162卷 / 03期

关键词：

D O I：

10.4064/sm162-3-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the BanachSaks property.

引用

页码：263 / 294

页数：32

共 35 条

[1] UNCONDITIONAL BASES AND MARTINGALES IN LP(F) [J].

ALDOUS, DJ .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1979, 85 (JAN) :117-123

[2]

Alexopoulos J., 1994, Quaest Math., V17, P231, DOI [10.1080/16073606.1994.9631762, DOI 10.1080/16073606.1994.9631762]

[3]

[Anonymous], 1982, TRANSL MATH MONOGR

[4] Systems of random variables equivalent in distribution to the Rademacher system and K-closed representability of Banach couples [J].

Astashkin, SV .

SBORNIK MATHEMATICS, 2000, 191 (5-6) :779-807

[5]

BAERNSTEIN A, 1972, STUD MATH, V17, P91

[6]

Banach S., 1930, STUD MATH, V2, P51

[7]

Bennett C., 1988, INTERPOLATION OPERAT

[8]

Carothers N.L., 1986, TEX FUNCT AN SEM 198, P107

[9] SUBSPACES OF LP,Q [J].

CAROTHERS, NL ;

DILWORTH, SJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 104 (02) :537-545

[10] The Kadec-Klee property in symmetric spaces of measurable operators [J].

Chilin, VI ;

Dodds, PG ;

Sukochev, FA .

ISRAEL JOURNAL OF MATHEMATICS, 1997, 97 (1) :203-219

← 1 2 3 4 →