Suppression-unconditional basic sequence ($\Vert {\sum }_{i\in A}{a}_i{e}_i\Vert \le C\Vert {\sum }_i{a}_i{e}_i\Vert$)

A basic sequence is suppression-unconditional with constant $C$ if every coordinate deletion satisfies the displayed inequality. When $C=1$, deletion never increases the norm. Uniformly bounded finite-coordinate projections imply unconditional convergence of the basis expansions; for real scalars, the sign-change constant is at most $2C$.