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On the Bishop-Phelps-Bollobás theorem for operators and numerical radius

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Kim S., Lee H., Martín M.

Studia Mathematica

2016

tom 233

nr 2

141-151

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].

Ograniczanie wyników

1 Studia Mathematica

1 Kim S.

1 Lee H.

1 Martín M.

1 2016

Wyniki wyszukiwania

On the Bishop-Phelps-Bollobás theorem for operators and numerical radius