Numerical index of vector-valued function spaces
Volume 142 / 2000
Studia Mathematica 142 (2000), 269-280
DOI: 10.4064/sm-142-3-269-280
Abstract
We show that the numerical index of a $c_0$-, $l_1$-, or $l_∞$-sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and $L_1(μ,X)$ (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
