The Bishop-Phelps-Bollobas theorem for L(L1(μ), L∞[0,1])

被引：23
作者：
Aron, Richard M. [2 ]
Choi, Yun Sung [3 ]
Garcia, Domingo [1 ]
Maestre, Manuel [1 ]
机构：
[1] Univ Valencia, Dept Anal Matemat, Burjassot 46100, Valencia, Spain
[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA
[3] POSTECH, Dept Math, Pohang 790784, South Korea
来源：
ADVANCES IN MATHEMATICS | 2011年 / 228卷 / 01期
关键词：
Operator; Norm attaining; Bishop-Phelps-Bollobas theorem; Measure space; NORM ATTAINING OPERATORS;
D O I：
10.1016/j.aim.2011.05.023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the Bishop-Phelps-Bollobas theorem holds for all bounded operators from L-1(mu) into L-infinity[0, 1], where mu is a sigma-finite measure. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：617 / 628
页数：12
相关论文
共 16 条
[1]   The Bishop-Phelps-Bolloba's theorem for operators [J].
Acosta, Maria D. ;
Aron, Richard M. ;
Garcia, Domingo ;
Maestre, Manuel .
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (11) :2780-2799
[2]   A multilinear Lindenstrauss theorem [J].
Acosta, MD ;
García, D ;
Maestre, M .
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (01) :122-136
[3]   There is no bilinear Bishop-Phelps theorem [J].
Acosta, MD ;
Aguirre, FJ ;
Paya, R .
ISRAEL JOURNAL OF MATHEMATICS, 1996, 93 :221-227
[4]  
ARON RM, 1995, LECT NOTES PURE APPL, V172, P19
[5]   A PROOF THAT EVERY BANACH SPACE IS SUBREFLEXIVE [J].
BISHOP, E ;
PHELPS, RR .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1961, 67 (01) :97-&
[6]  
Bollobas B., 1970, B LOND MATH SOC, V2, P181, DOI DOI 10.1112/BLMS/2.2.181
[7]   DENTABILITY AND PHELP,BISHOP PROPERTY [J].
BOURGAIN, J .
ISRAEL JOURNAL OF MATHEMATICS, 1977, 28 (04) :265-271
[8]   Norm or numerical radius attaining multilinear mappings and polynomials [J].
Choi, YS ;
Kim, SG .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1996, 54 :135-147
[9]  
DEFANT A, 1993, NORTH HOLLAND MATH S, V176
[10]   Norm attaining operators from L1 into L∞ [J].
Finet, C ;
Payá, R .
ISRAEL JOURNAL OF MATHEMATICS, 1998, 108 (1) :139-143
12