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.