Functional Analysis and Applications Seminar 

11/01/2013, 14:30 — 15:30 — Room P3.10, Mathematics Building
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, Cuernavaca, México

\(C^*\)-algebras of singular integral operators with shifts admitting distinct fixed points

Fredholm symbol calculi for the \(C^*\)-algebras \(\mathfrak{B}\) of singular integral operators with piecewise slowly oscillating coefficients extended by groups of unitary shift operators are constructed. The groups of unitary shift operators are associated with discrete amenable groups of piecewise smooth homeomorphisms that act topologically freely on the unit circle and admit distinct fixed points for different shifts. As a result, faithful representations of the quotient \(C^*\)-algebras \(\mathfrak{B}/{\mathfrak{K}}\), where \({\mathfrak {K}}\) is the ideal of compact operators, on suitable Hilbert spaces are constructed by applying the local-trajectory method, spectral measures and a lifting theorem, and Fredholm criteria for the operators \(B\in\mathfrak{B}\) are established.

The talk is based on a joint work with M. A. Bastos and C. A. Fernandes.