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arXiv · 1405.6428

The Bishop-Phelps-Bollob\'{a}s property for operators on $C(K)$

Maria D. Acosta
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Abstract

We provide a version for operators of the Bishop-Phelps-Bollob\'{a}s Theorem when the domain space is the complex space $C_0(L)$. In fact we prove that the pair $(C_0(L), Y)$ satisfies the Bishop-Phelps-Bollob\'{a}s 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 < \infty $).

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BibTeXRIS

Maria D. Acosta. 2014-05-25. The Bishop-Phelps-Bollob\'{a}s property for operators on $C(K)$. https://doi.org/10.1215/17358787-3492875

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