The Bishop-Phelps-Bollobas point property

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Dantas, Sheldon¹  Kim, Sun Kwang²  Lee, Han Ju³ 

[1] Univ Valencia, Dept Anal Matemat, Doctor Moliner 50, Burjassot 46100, Valencia, Spain

[2] Kyonggi Univ, Dept Math, Suwon 443760, South Korea

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

关键词: Bishop-Phelps theorem;    Bishop-Phelps-Bollobas property;    Norm attaining;    Bilinear forms;   

DOI  :  10.1016/j.jmaa.2016.07.009

来源: Elsevier

【 摘 要 】

In this article, we study a version of the Bishop-Phelps-Bollobas property. We investigate a pair of Banach spaces (X, Y) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop-Phelps-Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs (X, Y) which have and fail this property. Some stability results are obtained about l(1) and l(infinity) sums of Banach spaces and we also study this property for bilinear mappings. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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