Geodesic
Isomorphic and isometric copies of $\ell_\infty(\Gamma)$ in duals of Banach spaces and Banach lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 467-471 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\ell_\infty(\Gamma)$.
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 $\ell_\infty(\Gamma)$.
Classification : 46B04, 46B25, 46B42, 47B65
Keywords: isometry; embedding of $\ell_\infty$; dual space; Banach lattice 
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     author = {W\'ojtowicz, Marek},
     title = {Isomorphic and isometric copies of $\ell_\infty(\Gamma)$ in duals of {Banach} spaces and {Banach} lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {467--471},
     year = {2006},
     volume = {47},
     number = {3},
     mrnumber = {2281008},
     zbl = {1150.46004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a8/}
}
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Wójtowicz, Marek. Isomorphic and isometric copies of $\ell_\infty(\Gamma)$ in duals of Banach spaces and Banach lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 467-471. http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a8/