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Banach space properties of $ L\sp 1$ of a vector measure


Author: Guillermo P. Curbera
Journal: Proc. Amer. Math. Soc. 123 (1995), 3797-3806
MSC: Primary 46G10; Secondary 28B05, 46B20, 46E30
DOI: https://doi.org/10.1090/S0002-9939-1995-1285984-2
MathSciNet review: 1285984
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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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DOI: https://doi.org/10.1090/S0002-9939-1995-1285984-2
Article copyright: © Copyright 1995 American Mathematical Society

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