Banach space properties of 𝐿¹ of a vector measure

Curbera, Guillermo P.

doi:10.1090/S0002-9939-1995-1285984-2

Banach space properties of $L^ 1$ of a vector measure
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by Guillermo P. Curbera PDF

Proc. Amer. Math. Soc. 123 (1995), 3797-3806 Request permission

Abstract:

We consider the space ${L^1}(\nu )$ of real functions which are integrable with respect to a measure $\nu$ with values in a Banach space X. We study type and cotype for ${L^1}(\nu )$. We study conditions on the measure $\nu$ and the Banach space X that imply that ${L^1}(\nu )$ is a Hilbert space, or has the Dunford-Pettis property. We also consider weak convergence in ${L^1}(\nu )$.

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