# Metric approach to limit operators III

This is a continuation of my posts on the Spakula-Willett paper Metric approach to limit operators (see part I and part II).  In this post I will talk about “lower norm witnesses” on spaces with property A.  (This is quite close to what is done in my earlier post here, though using direct geometric tools rather than the functional analysis tricks I suggested, which only work in the Hilbert space case.)  Then in the next post I will talk about the “condensation of singularities” argument that completes the proof. Continue reading