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.