Norming points and critical points

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Cho, Dong Hoon¹  Choi, Yun Sung¹ 

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

关键词: Banach space;    Bishop-Phelps theorem;    Differentiation;    Critical point;   

DOI  :  10.1016/j.jmaa.2016.02.030

来源: Elsevier

【 摘 要 】

Using a diffeomorphism between the unit sphere and a closed hyperplane of an infinite dimensional Banach space, we introduce the differentiation of a function defined on the unit sphere, and show that a continuous linear functional attains its norm if and only if it has a critical point on the unit sphere. Furthermore, we provide a strong version of the Bishop-Phelps-BollobAs theorem for a Lipschitz smooth Banach space. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free