A Banach space dichotomy theorem for quotients of subspaces
Volume 180 / 2007
Studia Mathematica 180 (2007), 111-131
MSC: 46B03, 03E15.
DOI: 10.4064/sm180-2-2
Abstract
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.
