Bishop-Phelps-Bollobas moduli of a Banach space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Chica, Mario¹  Kadets, Vladimir²  Martin, Miguel¹  Moreno-Pulido, Soledad³  Rambla-Barreno, Fernando³ 

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

[2] Kharkiv VN Karazin Natl Univ, Dept Mech & Math, UA-61022 Kharkov, Ukraine

[3] Univ Cadiz, Dept Matemat, Puerto Real, Cadiz, Spain

关键词: Banach space;    Bounded linear operator;    Approximation;    Uniformly non-square spaces;   

DOI  :  10.1016/j.jmaa.2013.10.083

来源: Elsevier

【 摘 要 】

We introduce two Bishop-Phelps-Bollobas moduli of a Banach space which measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollobas theorem in this space. We show that there is a common upper bound for these moduli for all Banach spaces and we present an example showing that this bound is sharp. We prove the continuity of these moduli and an inequality with respect to duality. We calculate the two moduli for Hilbert spaces and also present many examples for which the moduli have the maximum possible value (among them, there are C(K) spaces and 1.1(mu) spaces). Finally, we show that if a Banach space has the maximum possible value of any of the moduli, then it contains almost isbmetric copies of the real space l(infinity)((2)).) and present an example showing that this condition is not sufficient. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free