Lipschitz factorization through subsets of Hilbert space

The Euclidean distortion of a metric space, a measure of how well the metric space can be embedded into a Hilbert space, is currently an active interdisciplinary research topic. We study the corresponding notion for mappings instead of spaces, which is that of Lipschitz factorization through subsets of Hilbert space. The main theorems are two characterizations of when a mapping admits such a factorization, both of them inspired by results dealing with linear factorizations through Hilbert space. The first is a nonlinear version of a classical theorem of Kwapień in terms of “dominated” sequences of vectors, whereas the second is a duality result by means of a tensor-product approach.