Unconditional basic sequence (source code)

= Unconditional basic sequence

An unconditional basic sequence is a <Schauder basis> for its closed span whose expansions converge after arbitrary permutations or coordinate suppressions. Equivalently, the finite coordinate projections are uniformly bounded. Failure of this property gives pairs of disjointly supported unit vectors at arbitrarily small distance, obtained by separating a finite combination with a large coordinate projection.