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 ${L^1}(\nu )$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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