We show that the numerical index of a -, -, or -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and (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.
@article{bwmeta1.element.bwnjournal-article-smv142i3p269bwm,
author = {Miguel Mart\'\i n and Rafael Pay\'a},
title = {Numerical index of vector-valued function spaces},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {269-280},
zbl = {0986.46022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p269bwm}
}
Martín, Miguel; Payá, Rafael. Numerical index of vector-valued function spaces. Studia Mathematica, Tome 141 (2000) pp. 269-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p269bwm/
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