Geodesic
The lattice copies of $\ell_1$ in Banach lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 649-653
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It is known that a Banach lattice with order continuous norm contains a copy of $\ell_1$ if and only if it contains a lattice copy of $\ell_1$. The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_0$- and $\ell_{\infty}$-cases considered by Lozanovskii, Mekler and Meyer-Nieberg.
It is known that a Banach lattice with order continuous norm contains a copy of $\ell_1$ if and only if it contains a lattice copy of $\ell_1$. The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_0$- and $\ell_{\infty}$-cases considered by Lozanovskii, Mekler and Meyer-Nieberg.
Classification : 46B42, 46B45
Keywords: Banach lattice; order continuous norm; embedding of $\ell_1$ 
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     author = {W\'ojtowicz, Marek},
     title = {The lattice copies of $\ell_1$ in {Banach} lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {649--653},
     year = {2001},
     volume = {42},
     number = {4},
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     zbl = {1090.46503},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_4_a5/}
}
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Wójtowicz, Marek. The lattice copies of $\ell_1$ in Banach lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 649-653. http://geodesic.mathdoc.fr/item/CMUC_2001_42_4_a5/