Category: Coarse Geometry

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"

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"