Banach Journal of Mathematical Analysis

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

María D. Acosta

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1458053864

Digital Object Identifier
doi:10.1215/17358787-3492875

Mathematical Reviews number (MathSciNet)
MR3474841

Zentralblatt MATH identifier
1347.46005

Subjects
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

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

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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