Embeddability of Snowflaked Metrics with Applications to the Nonlinear Geometry of the Spaces L-p and l(p) for 0 < p < infinity

摘要

We study the classical spaces L-p and l(p) for the whole range 0 < p < infinity from a metric viewpoint. As we go along, we look over some of the results and techniques that, together with our work in this paper, have permitted us to obtain a complete Lipschitz embeddability roadmap between any two of those spaces when equipped with their ad hoc distances and their snowflakings. Through connections with weaker forms of embeddings that lead to basic (yet fundamental) open problems, we also set the challenging goal of understanding the dissimilarities between the well-known subspace structure and the different nonlinear geometries that coexist inside L-p and l(p).