Common subspaces of 𝐿_{𝑝}-spaces

Koldobsky, Alexander

doi:10.1090/S0002-9939-1994-1195482-1

Common subspaces of $L_ p$-spaces
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Proc. Amer. Math. Soc. 122 (1994), 207-212 Request permission

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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