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

Abstract

We provide a version for operators of the Bishop-Phelps-Bollobás 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-Bollobás property for operators for every Hausdorff locally compact space $L$ and any $\mathbb{C}$-uniformly convex space. As a consequence, this holds for $Y=L_p(\mu )$ ($1\le p<\infty$).

13 pages

References in corpus (2)

• The Bishop-Phelps-Bollobás version of Lindenstrauss properties A and B
• Norm-attaining compact operators

Cited by in corpus (7)

• On the pointwise Bishop--Phelps--Bollobás property for operators
• Bishop-Phelps-Bollobás property for positive operators between classical Banach spaces
• A basis of ${\mathbb{R}}^n$ with good isometric properties and some applications to denseness of norm attaining operators
• Characterization of Banach spaces $Y$ satisfying that the pair $({\ell }_{\infty }^4,Y)$ has the Bishop-Phelps-Bollobás property for operators
• The Bishop-Phelps-Bollobás property on the space of $c_0$-sum
• The Birkhoff-James orthogonality and norm attainment for multilinear maps
• The Bishop-Phelps-Bollobás property for operators defined on $c_0$-sum of Euclidean spaces