The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces


Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c0, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobás property.

Publication Title

Journal of Nonlinear and Convex Analysis

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