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Numerical index of vector-valued function spaces

Miguel Martín, Rafael Payá (2000)

Studia Mathematica

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.

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