It is shown that there exists a Banach space with an unconditional basis which is not $c_0$-saturated, but whose dual is $\ell^1$-saturated.
@article{118858,
author = {Denny H. Leung},
title = {A note on Banach spaces with $\ell^1$-saturated duals},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {515-517},
zbl = {0881.46016},
mrnumber = {1426916},
language = {en},
url = {http://dml.mathdoc.fr/item/118858}
}
Leung, Denny H. A note on Banach spaces with $\ell^1$-saturated duals. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 515-517. http://gdmltest.u-ga.fr/item/118858/
Subspaces of $L^{p,q}$, Proc. Amer. Math. Soc. 104 (1988), 537-545. (1988) | MR 0962825
On $c_0$-saturated Banach spaces, Illinois J. Math. 39 (1995), 15-29. (1995) | MR 1299646
Classical Banach Spaces I, Springer-Verlag, 1977. | MR 0500056 | Zbl 0362.46013
Classical Banach Spaces II, Springer-Verlag, 1979. | MR 0540367 | Zbl 0403.46022