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

• Autorzy: Sun Kwang Kim , Han Ju Lee , Miguel Martín
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 141-151

Daty

wydano

2016

Twórcy

autor

Sun Kwang Kim

• Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea

autor

Han Ju Lee

• Department of Mathematics Education, Dongguk University - Seoul, 04620 Seoul, Republic of Korea

autor

Miguel Martín

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm8311-4-2016