Starts 28 Apr 2011 16:00
Ends 28 Apr 2011 20:00
Central European Time
ICTP
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11 I - 34151 Trieste (Italy)
The spectral unit ball of dimension n^2 is the set of all n\times n matrices having spectral radius less than 1. This object is of some prominence in linear control-theory circles because the Pick-Nevanlinna interpolation problem on it is very challenging. A first step in solving this problem would be to solve the 2-point problem, i.e. to produce a Schwarz lemma for the spectral unit ball. This is hard because the spectral unit ball is non-homogeneous when n>1, but there have been some recent results which we shall discuss. The complex geometry of the spectral unit ball in n^2 (n>1) is interesting because GL(n,C) acts non-trivially on it by conjugation. We shall discuss how this feature points to the prospect of a sharp Schwarz lemma.
  • A. Bergamo