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- W3103308971 abstract "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 $qneq 2$ turns out to be much more restrictive. The main result combined with a result of Dor provides a proof of the fact that if $qneq 2$ 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." @default.
- W3103308971 created "2020-11-23" @default.
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- W3103308971 date "2020-05-05" @default.
- W3103308971 modified "2023-10-17" @default.
- W3103308971 title "On a question of Pietch" @default.
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- W3103308971 doi "https://doi.org/10.1007/s11117-020-00758-6" @default.
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