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 we give examples of such spaces. Moreover, for any compact subset $Q$ of $(0,\infty)\setminus \{ 2k, k\in N\},$ we can construct a space isometric to subspaces of $L_{ q}$ for all $q\in Q$ simultaneously. This paper requires vanilla.sty
Categories: math.FA