On the Bishop-Phelps-Bollobás theorem for operators and numerical radius
Studia Mathematica, Tome 233 (2016) no. 2, p. 141.

Voir la notice de l'article dans European Digital Mathematics Library

We study the Bishop-Phelps-Bollobás property for numerical radius (for short, BPBp-nu) of operators on ℓ₁-sums and ℓ ∞ -sums of Banach spaces. More precisely, we introduce a property of Banach spaces, which we call strongly lush. We find that if X is strongly lush and X ⊕₁ Y has the weak BPBp-nu, then (X,Y) has the Bishop-Phelps-Bollobás property (BPBp). On the other hand, if Y is strongly lush and X ⊕ ∞ Y has the weak BPBp-nu, then (X,Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L₁(μ) spaces, and finite-codimensional subspaces of C[0,1].
Classification : 46B04, 46B20, 46B22
Mots-clés : Banach space, approximation, numerical radius attaining operators, Bishop-Phelps-Bollob'as theorem 
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Sun Kwang Kim; Han Ju Lee; Miguel Martín. On the Bishop-Phelps-Bollobás theorem for operators and numerical radius. Studia Mathematica, Tome 233 (2016) no. 2, p. 141. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_2_285608/