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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak sequential convergence in $ L\sb{E}\sp{\infty }$ and Dunford-Pettis property of $ L\sb{E}\sp{1}$


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 78 (1980), 85-88
MSC: Primary 28B05; Secondary 46G10
MathSciNet review: 548089
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Abstract: For a $ \sigma $-finite measure space $ (X,\mathfrak{A},\mu )$ it is proved that weak sequential convergence in $ L_E^\infty $ implies almost everywhere pointwise convergence, with the weak topology on the Banach space E. Also it is proved that if weak and norm sequential convergence coincide in $ E'$, then $ L_E^1$ has the Dunford-Pettis property.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0548089-0
Article copyright: © Copyright 1980 American Mathematical Society