On spaces admitting no ℓ p or c 0 spreading model

Abstract

It is shown that for each separable Banach space X not admitting l1 as a spreading model there is a space Y having X as a quotient and not admitting any lp for 1 ≤ p < ∞ or c0 as a spreading model. We also include the solution to a question of Johnson and Rosenthal (Studia Math 43:77–92, 1972) on the existence of a separable space not admitting as a quotient any space with separable dual.