Abstract
The C∗-algebra \(\mathfrak{B}\) of bounded linear operators on the space \({L}^{2}(\mathbb{T})\), which is generated by all multiplication operators by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of a group G of orientation-preserving diffeomorphisms of \({\mathbb{T}}\) onto itself that have the same finite set of fixed points for all \({g} \in {G} {\backslash} \{e\}\), is studied. A Fredholm symbol calculus for the C∗-algebra \(\mathfrak{B}\) and a Fredholm criterion for the operators \({B} \in \mathfrak{B}\) are established by using spectral measures and the local-trajectory method for studying C∗-algebras associated with C∗-dynamical systems.
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