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$$L_ 1$$ contains every two-dimensional normed space. (English) Zbl 0679.46016
Quite elementary proofs of the following two facts are given:
(1) every 2-dimensional (real) normed space embeds linearly and isometrically in $$L_ 1(0,1);$$
(2) $$\ell_{\infty}(3)$$ is not isometric to any subset of $$L_ 1(0,1)$$.
Reviewer: S.V.Kislyakov

##### MSC:
 46B25 Classical Banach spaces in the general theory
##### Keywords:
isometric imbeddings
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