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Proceedings of the American Mathematical Society

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A note on the spaces $L_{p}$ 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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Keywords: <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="${L_p}$">-spaces, <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-normed spaces, dual spaces
Article copyright: © Copyright 1976 American Mathematical Society