Adobe InDesign CC 2018 (v16.0) X86-x64 ((EXCLUSIVE)) Full Version

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Published: September 9, 2022 (3 weeks ago)
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Adobe InDesign CC 2018 (v16.0) X86-x64 ((EXCLUSIVE)) Full Version

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Adobe InDesign CC 2018 (v16.0) X86-x64 Full Version

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Isometric embedding into a space whose dual is not finite

I have a problem in the construction of an isometric embedding of $ell_2$ into a space whose dual is not finite. I appreciate if you could help me.

A:

Let $X$ be a Banach space with a Schauder basis $(e_n)_{n=1}^infty$ and fix $p in (1, infty)$. Let $Y$ be a Banach space such that $Y^star$ is non-separable. Then there is an isometric embedding of $X$ into $Y$ (and such an embedding is unique). This fact follows from the fact that the set of bounded linear operators $X to Y$ which preserve the norm is linearly isomorphic to $Y^star$ (see e.g. p. 106 of this paper).

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