Abstract
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.
Original language | English |
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Pages (from-to) | 243-249 |
Number of pages | 7 |
Journal | Journal of Nonlinear and Convex Analysis |
Volume | 17 |
Issue number | 2 |
State | Published - Feb 2016 |
Keywords
- Approximation
- Banach space
- Bishop-Phelps-Bollobás theorem
- Norm-attaining operators