Banach Journal of Mathematical Analysis

The Bishop–Phelps–Bollobás property for operators on C(K)

María D. Acosta

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We provide a version for operators of the Bishop–Phelps–Bollobás theorem when the domain space is the complex space C0(L). In fact, we prove that the pair (C0(L),Y) will satisfy the Bishop–Phelps–Bollobás property for operators for every Hausdorff locally compact space L and any C-uniformly convex space. As a consequence, this holds for Y=Lp(μ) (1p<).

Article information

Banach J. Math. Anal., Volume 10, Number 2 (2016), 307-319.

Received: 11 March 2015
Accepted: 9 June 2015
First available in Project Euclid: 15 March 2016

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Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47B99: None of the above, but in this section 46B25: Classical Banach spaces in the general theory

Banach space norm-attaining operator denseness of norm-attaining operators Bishop–Phelps–Bollobás property


Acosta, María D. The Bishop–Phelps–Bollobás property for operators on $\mathcal{C}(K)$. Banach J. Math. Anal. 10 (2016), no. 2, 307--319. doi:10.1215/17358787-3492875.

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