NUMERICAL INDEX AND THE DAUGAVET PROPERTY FOR $L_infty(mu,X)$

[摘要] We prove that the space $L_infty(mu,X)$ has the same numerical index as the Banach space $X$ for every $sigma$-finite measure $mu$. We also show that $L_infty(mu,X)$ has the Daugavet property if and only if $X$ has or $mu$ is atomless.AMS 2000 Mathematics subject classification: Primary 46B20; 47A12

[学科分类] 数学（综合）

[关键词] Daugavet property;numerical index;numerical radius