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Proceedings of the American Mathematical Society

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



Common subspaces of $ L\sb p$-spaces

Author: Alexander Koldobsky
Journal: Proc. Amer. Math. Soc. 122 (1994), 207-212
MSC: Primary 46E30; Secondary 46B04
MathSciNet review: 1195482
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Abstract: For $ n \geq 2,p < 2$, and $ q > 2$ does there exist an n-dimensional Banach space different from Hilbert spaces which is isometric to subspaces of both $ {L_p}$ and $ {L_q}$? Generalizing the construction from the paper Zonoids whose polars are zonoids by R. Schneider (Proc. Amer. Math. Soc. 50 (1975), 365-368) we give examples of such spaces. Moreover, for any compact subset Q of $ (0,\infty )\backslash \{ 2k,k \in N\} $ we can construct a space isometric to subspaces of $ {L_q}$ for all $ q \in Q$ simultaneously.

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Keywords: Isometries, positive definite functions, spherical harmonics
Article copyright: © Copyright 1994 American Mathematical Society