6533b828fe1ef96bd12885f7

RESEARCH PRODUCT

The Bishop–Phelps–Bollobás theorem for operators

Manuel MaestreMaría D. AcostaRichard M. AronDomingo García

subject

Discrete mathematicsPure mathematicsMathematics::Functional AnalysisApproximation propertyEberlein–Šmulian theoremBanach spaceNorm attainingBishop–Phelps theoremUniform boundedness principleUniform convexityInterpolation spaceOperatorClosed graph theoremReflexive spaceBishop–Phelps theoremAnalysisMathematics

description

AbstractWe prove the Bishop–Phelps–Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop–Phelps–Bollobás theorem holds for operators from ℓ1 into Y. Several examples of classes of such spaces are provided. For instance, the Bishop–Phelps–Bollobás theorem holds when the range space is finite-dimensional, an L1(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.

yearjournalcountryeditionlanguage
2008-06-01Journal of Functional Analysis
10.1016/j.jfa.2008.02.014http://dx.doi.org/10.1016/j.jfa.2008.02.014