Rubén A. Martínez-Avendaño - Some spectral properties of Hankel operators

We define Hankel operators and mention some of their basic properties. We discuss the proof of the following theorem: Given any compact subset of the complex plane containing zero, there exists a Hankel operator having this set as its spectrum. This theorem was first proven by Sergei Treil' a few years ago, but never published. With Treil's collaboration, we have written a detailed proof of the theorem.