C*-algebras of singular integral operators with shifts having the
same nonempty set of periodic points
The C*-subalgebra of bounded linear operators on the
space over the unit circle 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 onto itself
with any nonempty set of common periodic points is studied. A
symbol calculus for the C*-algebra and a Fredholm criterion for
its elements are obtained. For the C*-algebra composed by all
functional operators in , an invertibility criterion for its
elements is also established. Both the C*-algebras and 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.
