Block basic sequence
= Block basic sequence
Relative to a <Schauder basis> $(e_j)$, a block basic sequence consists of nonzero finite combinations supported on successive disjoint coordinate intervals. In the <l-p sequence space>, disjointly supported vectors $u_n$ of norm one satisfy $\|\sum a_nu_n\|_p^p=\sum|a_n|^p$. Their closed span is consequently isometric to the <l-p sequence space>.