A note on the intersection of Banach subspaces
In this article, the authors prove that a Banach space \(X\) is reflexive if and only if, for every \(x \in X\) and every decreasing sequence \((X_n)\) of closed subspaces of \(X\), \(d(x,\bigcap_{n=1}^\infty X_n) = \lim_{n\to\infty} d(x,X_n)\) where \(d(x,C)\) denotes the distance from \(x\) to \(C\).
scientific article; zbMATH DE number 2113000