## Banach Journal of Mathematical Analysis

### The Bishop–Phelps–Bollobás property for operators on $\mathcal{C}(K)$

María D. Acosta

#### Abstract

We provide a version for operators of the Bishop–Phelps–Bollobás theorem when the domain space is the complex space $\mathcal{C}_{0}(L)$. In fact, we prove that the pair $(\mathcal{C}_{0}(L),Y)$ will satisfy the Bishop–Phelps–Bollobás property for operators for every Hausdorff locally compact space $L$ and any $\mathbb{C}$-uniformly convex space. As a consequence, this holds for $Y=L_{p}(\mu)$ ($1\le p\lt \infty$).

#### Article information

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

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

https://projecteuclid.org/euclid.bjma/1458053864

Digital Object Identifier
doi:10.1215/17358787-3492875

Mathematical Reviews number (MathSciNet)
MR3474841

Zentralblatt MATH identifier
1347.46005

#### Citation

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. https://projecteuclid.org/euclid.bjma/1458053864

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