Functional Analysis and Applications Seminar 

21/04/2006, 14:30 — 16:00 — Room P3.10, Mathematics Building
Cristina Câmara, Instituto Superior Técnico, U.T. Lisboa

Fredholmness and corona problems

The Fredholm properties of Toeplitz operators with \(2\times 2\) matrix symbols \(G\), which are essentially bounded on the real line, are studied in connection with some properties of a solution to a homogeneous linear Riemann-Hilbert problem with coefficient \(G\). Conditions for the Toeplitz operator to be Fredholm are obtained and, if that is the case, formulas for the factors in a generalized factorization of \(G\) are given in terms of the solutions to a pair of non-standard corona problems. These results are used to establish partial index estimates for Daniele-Khrapkov matrix functions.