The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite

摘要

Let X be a normed space that satisfies the Johnson-Lindenstrauss lemma (J--L lemma, in short) in the sense that for any integer n and any x1,...,xn ε X there exists a linear mapping L: X → F, where F ⊆ X is a linear subspace of dimension O(log n), such that