### A Banach space dichotomy theorem for quotients of subspaces

A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.