### About polynomially bounded operators and invariant subspaces

- Series
- Analysis Seminar
- Time
- Friday, May 4, 2012 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Professor Bernard Chevreau – University of Bordeaux 1

In the first part of the talk we will give a brief survey of significant
results going from S. Brown pioneering work showing the existence of
invariant subspaces for subnormal operators (1978) to Ambrozie-Muller
breakthrough asserting the same conclusion for the adjoint of a
polynomially bounded operator (on any Banach space) whose spectrum
contains the unit circle (2003). The second part will try to give some
insight of the different techniques involved in this series of results,
culminating with a brilliant use of Carleson interpolation theory for
the last one. In the last part of the talk we will discuss additional
open questions which might be investigated by these techniques.