Bases equivalent to the unit vector basis of $c_0$ or $\ell_p$

Abstract

We will show that an unconditional basis in a Banach space is equivalent to the unit vector basis of $c_0$ or $\ell_p$ for $1\le p < \infty$ if and only if all finitely supported blocks of the basis generated by a unit vector and its dual basis are uniformly equivalent to the basis or all such blocks are uniformly complemented.