Frames for Metric Spaces

We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric 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.

Automated summary

We conducted a systematic study on frames for metric spaces, proving that every separable metric space can be measured by a metric M-d-frame. Through Lipschitz-free Banach spaces, we established a correspondence between frames for metric spaces and frames for subsets of Banach spaces. We derived characterizations and stability results for metric frames.