Abstract
In this paper we show that the Bishop-Phelps-Bollobás theorem holds for L(L1(μ),L1(ν)) for all measures μ and ν and also holds for L(L1(μ),L∞(ν)) for every arbitrary measure μ and every localizable measure ν. Finally, we show that the Bishop-Phelps-Bollobás theorem holds for two classes of bounded linear operators from a real L1(μ) into a real C(K) if μ is a finite measure and K is a compact Hausdorff space. In particular, one of the classes includes all Bochner representable operators and all weakly compact operators.
Original language | English |
---|---|
Pages (from-to) | 214-242 |
Number of pages | 29 |
Journal | Journal of Functional Analysis |
Volume | 267 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jul 2014 |
Keywords
- Approximation
- Banach space
- Bishop-Phelps-Bollobás theorem
- Norm-attaining operators