On spaces admitting no ℓ p or c 0 spreading model

Abstract

Abstract. It is shown that for each separable Banach space X not admitting ℓ 1 as a spreading model there is a space Y having X as a quotient and not admitting any ℓp for 1 ≤ p < ∞ or c 0 as a spreading model.We also include the solution to a question of W.B. Johnson and H.P. Rosenthal on the existence of a separable space not admitting as a quotient any space with separable dual.

ξ-completely continuous operators and ξ-Schur Banach spaces

“…In this section, we perform a contruction of a transfinite modification of spaces studied by Argyros and Beanland [2], which were themselves modifications of a space constructed by Odell and Schlumprecht [25] of a Banach space which admits no c 0 or ℓ p spreading model.…”