Frames for Metric Spaces

Abstract

We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric ${\mathcal{M}}_d$-frame. Through Lipschitz-free Banach spaces we show that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. We derive some characterizations of metric frames. We also derive stability results for metric frames.

22 pages