Diamond-graph characterization of superreflexivity
= Diamond-graph characterization of superreflexivity
A Banach space $X$ is superreflexive exactly when the distortions $c_X(D_n)$ of the finite diamond graphs tend to infinity. A uniformly separated convex-block sequence recursively realizes all branches of $D_n$ with bounded distortion, while uniform convexity forces quantitative collapse across repeated diamonds.