Gowers dichotomy theorem
= Gowers dichotomy theorem
{c}
Every infinite-dimensional <Banach space> contains either an <unconditional basic sequence> or a <hereditarily indecomposable Banach space>. For a space with a basis and no unconditional basic sequence, apply the block Ramsey theorem to finite sequences whose odd and even spans contain nearby unit vectors. A diagonal sequence of successively sharper games gives a subspace in which every pair of infinite-dimensional subspaces has angle zero.