The lattice copies of $\ell_1$ in Banach lattices
Wójtowicz, Marek
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 649-653 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  46B42,  46B45 
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     author = {Marek W\'ojtowicz},
     title = {The lattice copies of $\ell\_1$ in Banach lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {649-653},
     zbl = {1090.46503},
     mrnumber = {1883374},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119281}
}

Wójtowicz, Marek. The lattice copies of $\ell_1$ in Banach lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 649-653. http://gdmltest.u-ga.fr/item/119281/

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