Functional Analysis and Applications Seminar 

26/03/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Cristina Diogo, Instituto Superior de Ciências do Trabalho e da Empresa, Lisboa

Fredholm properties of Toeplitz operators and corona problems (I)

The invertibility and Fredholmness of Toeplitz operators with $2\times 2$ matrix symbol $G$ can be studied in connection with some properties of a solution to a Riemann-Hilbert problem with coefficient $G$. We show that from this solution we can obtain formulas for the factors of a Wiener-Hopf factorization of $G$, when it exists, which allows us to construct a generalized inverse for the Toeplitz operator. This is the first of a pair of talks on this subject based on joint work with M. C. Câmara.