= Unconditional tree index
{title2=$o(T_C(X))$}
Let $T_C(X)$ consist of finite normalized sequences for which every scalar combination and sign change satisfy $\|\sum_i\varepsilon_i a_ix_i\|\leq C\|\sum_i a_ix_i\|$. These inequalities give a closed <tree on a Polish space> when $X$ is separable. An infinite branch is an <unconditional basic sequence>. If there is no such sequence, each fixed-constant tree is well-founded and has countable <rank of a well-founded tree>. Consequently, finite unconditional configurations with one fixed constant and arbitrarily high countable ranks force an infinite unconditional sequence.
Back to article page
