On a question of Haskell P. Rosenthal

Abstract

We consider a normalized basis in a Banach space with the following property: any normalized block sequence of the basis has a subsequence equivalent to the basis. We show that under uniformity or other natural assumptions, a basis with this property is equivalent to the unit vector basis of $c_0$ or ${\ell }_p$. We also address an analogous problem for spreading models.

14 pages