Functional Analysis and Applications Seminar 

06/07/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Yuri I. Karlovich, Universidad Autónoma del Estado de Morelos, México

C*-algebras of singular integral operators with shifts having the same nonempty set of periodic points

The C*-subalgebra $B$ of bounded linear operators on the $L^2$ space over the unit circle $T$ which is generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of an amenable group of orientation-preserving diffeomorphisms (shifts) of $T$ onto itself with any nonempty set of common periodic points is studied. A symbol calculus for the C*-algebra $B$ and a Fredholm criterion for its elements are obtained. For the C*-algebra $A$ composed by all functional operators in $B$, an invertibility criterion for its elements is also established. Both the C*-algebras $B$ and $A$ are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure. The results essentially depend on the structure of the set of periodic points of shifts. The talk is related to a joint work with M.A. Bastos and C.A.Fernandes.