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Proceedings of the American Mathematical Society

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A note on the spaces $ L\sb{p}$ for $ 0<p\leq 1$


Author: N. J. Kalton
Journal: Proc. Amer. Math. Soc. 56 (1976), 199-202
MSC: Primary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1976-0438103-4
MathSciNet review: 0438103
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Abstract: It is shown that there is no Hausdorff vector topology $ \rho $ on the space $ {L_p}$ (where $ 0 < p \leqslant 1$) such that the unit ball of $ {L_p}$ is relatively compact for the topology $ \rho $.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0438103-4
Keywords: $ {L_p}$-spaces, $ p$-normed spaces, dual spaces
Article copyright: © Copyright 1976 American Mathematical Society