Unconditionality in spaces of smooth functions

被引:3
作者
Godefroy, Gilles [1 ]
机构
[1] Univ Paris 06, CNRS, Inst Math Jussieu 175, F-75013 Paris, France
关键词
Subspaces of spaces with unconditional bases; Muntz spaces; Banach spaces of smooth functions; BANACH-SPACES; SUBSPACES; IDEALS;
D O I
10.1007/s00013-009-3037-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Our main result shows that subspaces of L(1)([0, 1]) on which the blow-up operators act compactly are isometric to dual spaces, and their natural predual belongs to the Banach-Mazur closure of quotient spaces of c(0)(N). Related general results are shown for subspaces X of C(0)(Omega) or of reflexive Kothe function spaces, which imply that when X consists of smooth functions it embeds into a Banach space with an unconditional basis.
引用
收藏
页码:476 / 484
页数:9
相关论文
共 18 条
[1]  
Al Alam I, 2008, P AM MATH SOC, V136, P193
[2]  
Al-Alam I., 2008, THESIS U LENS
[3]  
[Anonymous], 1991, CAMBRIDGE STUDIES AD
[4]  
BORWEIN P, 1995, GRADUATES TEXTS MATH, V161
[5]  
COWELL SR, 2008, ASYMPTOTIC UNCONDITI
[6]   Subspaces of Lp isometric to subspaces of lp [J].
Delbaen, F ;
Jarchow, H ;
Pelczynski, A .
POSITIVITY, 1998, 2 (04) :339-367
[7]   WELL-ARRANGED SUBSPACES OF L1-APPLICATIONS [J].
GODEFROY, G .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 286 (01) :227-249
[8]  
Godefroy G, 1996, J REINE ANGEW MATH, V471, P43
[9]  
GODEFROY G, 1993, STUD MATH, V104, P13
[10]  
Gurariy V.I., 2005, LECT NOTES MATHS, V1870