On spaces admitting no ${\ell }_p$ or $c_0$ spreading model

Abstract

It is shown that for each separable Banach space $X$ not admitting ${\ell }_1$ as a spreading model there is a space $Y$ having $X$ as a quotient and not admitting any ${\ell }_p$ for $1\le p<\infty$ 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.

17 pages

References in corpus (2)

• Finite order spreading models
• On the hereditary proximity to ${\ell }_1$