### Quasi-local operators

In the first post of this series we asked at the end two questions – in this post we start working towards the answers in the general setup of the third post of this series. Our setup from the third post is the following: We have a metric space $$(X,d)$$ and we consider a bounded, … Continue reading "Quasi-local operators"

### AMS Special Session on the Mathematics of John Roe

There was a Special Session on Coarse Geometry, Index Theory, and Operator Algebras: Around the Mathematics of  John Roe at the Spring Central and Western Joint Sectional Meeting of the AMS last weekend to which Christopher and I were invited to give talks. John Roe passed away last year. His personal webpage is still online … Continue reading "AMS Special Session on the Mathematics of John Roe"

### Operators of finite propagation

In the starting post of this series we considered infinite band matrices (with uniformly bounded entries) acting on infinite vectors and asked at the end the question how to determine whether a given matrix, which is not a band matrix, can be approximated by such. Today we provide the setup in order to answer this question properly in … Continue reading "Operators of finite propagation"

### Equivariant band matrices and Fourier series

Recall that in the first post of this series we claimed that there exists an infinite matrix $$T$$ which is in the closure (in operator norm) of the band matrices with uniformly bounded entries, but for which we have $$\|T^{(R)}\| \to \infty$$. Here \[T^{(R)}_{m,n} := \begin{cases} T_{m,n} & \text{ if } |m-n| \le R\\ 0 & … Continue reading "Equivariant band matrices and Fourier series"

### Norms of infinite matrices

This is the first post of a series of posts in which we will eventually venture deep into the realm of coarse geometry. But we will always be motivated by questions which are related to the one that we will discuss here. But our first steps into coarse geometry will be very gently: we will … Continue reading "Norms of infinite matrices"