In the first post in this series, I gave some background to the “Big Question” on limit operators which it appears that Lindner and Seidel have solved for the case of free abelian groups. In the next couple of posts I want to sketch some of the key ideas of their proof and to explore to what extent it can also be generalized to all exact groups (in the same way that I generalized the basic theory of limit operators to all exact groups in my 2005 paper).
There are two components to the L-S argument, it seems to me.
- a localization property for the “lower norm” of a finite propagation operators, and
- a “condensation of singularities” argument.
In this post we’ll look at the first of those. Continue reading