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.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_2006__47_3_a8,
     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},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2006},
     mrnumber = {2281008},
     zbl = {1150.46004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a8/}
}
TY  - JOUR
AU  - Wójtowicz, Marek
TI  - Isomorphic and isometric copies of $\ell_\infty(\Gamma)$ in duals of Banach spaces and Banach lattices
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 467
EP  - 471
VL  - 47
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a8/
LA  - en
ID  - CMUC_2006__47_3_a8
ER  - 
%0 Journal Article
%A Wójtowicz, Marek
%T Isomorphic and isometric copies of $\ell_\infty(\Gamma)$ in duals of Banach spaces and Banach lattices
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 467-471
%V 47
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a8/
%G en
%F CMUC_2006__47_3_a8
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/