6533b832fe1ef96bd129ac92
RESEARCH PRODUCT
Some kind of Bishop-Phelps-Bollobás property
Sheldon Dantassubject
Mathematics::Functional AnalysisPure mathematicsProperty (philosophy)Approximation propertyGeneral Mathematics010102 general mathematicsRegular polygonBanach space010103 numerical & computational mathematicsType (model theory)Characterization (mathematics)01 natural sciencesCombinatoricsBounded function0101 mathematicsBishop–Phelps theoremMathematicsdescription
In this paper we introduce two Bishop–Phelps–Bollobas type properties for bounded linear operators between two Banach spaces X and Y: property 1 and property 2. These properties are motivated by a Kim–Lee result which states, under our notation, that a Banach space X is uniformly convex if and only if the pair (X,K) satisfies property 2. Positive results of pairs of Banach spaces (X,Y) satisfying property 1 are given and concrete pairs of Banach spaces (X,Y) failing both properties are exhibited. A complete characterization of property 1 for the pairs (lp,lq) is also provided.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-10-05 | Mathematische Nachrichten |