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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
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