Geodesic
Banach spaces with a supershrinking basis
Studia Mathematica, Tome 132 (1999) no. 1, pp. 29-36

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without $c_0$ copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the $c_0$-theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in $c_0$.
DOI : 10.4064/sm-132-1-29-36

Ginés López 1

1 
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Ginés López. Banach spaces with a supershrinking basis. Studia Mathematica, Tome 132 (1999) no. 1, pp. 29-36. doi: 10.4064/sm-132-1-29-36

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