The Bishop-Phelps-Bollobas property for operators between spaces of continuous functions

被引：17

作者：

Acosta, Maria D. ^{[1
]}

Becerra-Guerrero, Julio ^{[1
]}

Choi, Yun Sung ^{[2
]}

Ciesielski, Maciej ^{[3
]}

Kim, Sun Kwang ^{[4
]}

Lee, Han Ju ^{[5
]}

Lourenco, Mary Lilian ^{[6
]}

Martin, Miguel ^{[1
]}

机构：

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

[2] POSTECH, Dept Math, Pohang 790784, South Korea

[3] Poznan Univ Tech, PL-60965 Poznan, Poland

[4] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea

[5] Dongguk Univ Seoul, Dept Math Educ, Seoul 100715, South Korea

[6] Univ Sao Paulo, Inst Matemat & Estat, BR-05311970 Sao Paulo, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 95卷

基金：

巴西圣保罗研究基金会; 新加坡国家研究基金会;

关键词：

Banach space; Optimization; Norm-attaining operators; Bishop-Phelps theorem; Bishop-Phelps-Bollobas theorem; BANACH-SPACES; THEOREM; L1;

D O I：

10.1016/j.na.2013.09.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobas property. A similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and Hausdorff topological space into a uniformly convex space, and for the class of compact operators from a Banach space into a predual of an L-1-space. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：323 / 332

页数：10

共 19 条

[1]

Acosta M.D., 2013, PREPRINT

[2] 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

[3] THE BISHOP-PHELPS-BOLLOBAS THEOREM FOR BILINEAR FORMS [J].

Acosta, Maria D. ;

Becerra-Guerrero, Julio ;

Garcia, Domingo ;

Maestre, Manuel .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (11) :5911-5932

[4] THE BISHOP-PHELPS-BOLLOBAS THEOREM AND ASPLUND OPERATORS [J].

Aron, R. M. ;

Cascales, B. ;

Kozhushkina, O. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (10) :3553-3560

[5]

Aron R.M., 2013, PREPRINT

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

Aron, Richard M. ;

Choi, Yun Sung ;

Garcia, Domingo ;

Maestre, Manuel .

ADVANCES IN MATHEMATICS, 2011, 228 (01) :617-628

[7] A PROOF THAT EVERY BANACH SPACE IS SUBREFLEXIVE [J].

BISHOP, E ;

PHELPS, RR .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1961, 67 (01) :97-&

[8]

Bollobas B., 1970, B LOND MATH SOC, V2, P181, DOI DOI 10.1112/BLMS/2.2.181

[9] A Bishop-Phelps-Bollobas type theorem for uniform algebras [J].

Cascales, B. ;

Guirao, A. J. ;

Kadets, V. .

ADVANCES IN MATHEMATICS, 2013, 240 :370-382

[10]

Chica M., 2013, PREPRINT

← 1 2 →