论文标题
关于彼得的问题
On a question of Pietch
论文作者
论文摘要
主要的结果是，有限的尺寸标准空间在$ \ ell_p $中嵌入$ \ ell_p $，并且仅当它具有离散的征税$ p $ - 代表。这为Pietch提出的问题提供了替代答案，作为推论，这是一个简单的证明，即除非$ p $是整数，否则二维Hilbert Space $ \ ell_2^2 $不是等于$ \ ell_p $的子空间。 $ \ ell_q^2 $带有$ q \ neq 2 $的情况更加限制。结合DOR的结果的主要结果提供了以下事实证明：如果$ q \ neq 2 $，则$ \ ell_q^2 $不是$ \ ell_p $的子空间等均值，除非$ q = p $。还包括有关$ \ ell_p $的有限尺寸子空间平滑度的限制程度的进一步申请。
The main result is that a finite dimensional normed space embeds isometrically in $\ell_p$ if and only if it has a discrete Levy $p$-representation. This provides an alternative answer to a question raised by Pietch, and as a corollary, a simple proof of the fact that unless $p$ is an even integer, the two-dimensional Hilbert space $\ell_2^2$ is not isometric to a subspace of $\ell_p$. The situation for $\ell_q^2$ with $q\neq 2$ turns out to be much more restrictive. The main result combined with a result of Dor provides a proof of the fact that if $q\neq 2$ then $\ell_q^2$ is not isometric to a subspace of $\ell_p$ unless $q=p$. Further applications concerning restrictions on the degree of smoothness of finite dimensional subspaces of $\ell_p$ are included as well.
