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Keywords:
isometry; embedding of $\ell_\infty$; dual space; Banach lattice
isometry; embedding of $\ell_\infty$; dual space; Banach lattice
Summary:
Let $X$ and $E$ be a Banach space and a real Banach lattice, respectively, and let $\Gamma$ denote an infinite set. We give concise proofs of the following results: (1) The dual space $X^*$ contains an isometric copy of $c_0$ iff $X^*$ contains an isometric copy of $\ell_\infty $, and (2) $E^*$ contains a lattice-isometric copy of $c_0(\Gamma)$ iff $E^*$ contains a lattice-isometric copy of $\ell_\infty(\Gamma)$.
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