Characterization of Banach spaces Y satisfying that the pair (l∞4, Y) has the Bishop-Phelps-Bollobas property for operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Acosta, Maria D.¹  Davila, Jose L.²  Soleimani-Mourchehkhorti, Maryam³ 

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

[2] Univ Los Andes, Fac Ciencias, Dept Matemat, Merida 5101, Venezuela

[3] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

关键词: Banach space;    Bishop-Phelps theorem;    Norm attaining operator;    Bishop-Phelps-Bollobas property;   

DOI  :  10.1016/j.jmaa.2018.06.032

来源: Elsevier

【 摘 要 】

We study the Bishop-Phelps-Bollobas property for operators from l(infinity)(4), to a Banach space. For this reason we introduce an appropriate geometric property, namely the AHSp-l(infinity)(4). We prove that spaces Y satisfying AHSp-l(infinity)(4) are precisely those spaces Y such that (l(infinity)(4), Y) has the Bishop-Phelps-Bollobas property. We also provide classes of Banach spaces satisfying this condition. For instance, finite-dimensional spaces, uniformly convex spaces, C-0 (L) and L-1(mu) satisfy AHSp-l(infinity)(4). (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free