I am looking for a standard name (if it exists) for the following property of a Schauder basis $ (e_i)_{i=1}^\infty$ in a Banach space $ X$ : $ $ \|\sum_{i\in F}x_ie_i\|\le\|x\|$ $ for any $ x=\sum_{i=1}^\infty x_ie_i\in X$ and any finite subset $ F\subset\mathbb N$ . This condiion implies that the Schauder basis is unconditional.Read more