On the C^*-Algebra Generated by the Bergman Operator, Carleman Second-Order Shift, and Piecewise Continuous Coefficients - Mozel’, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
We study the C^* -algebra generated by the Bergman operator with piecewise continuous coefficients in the Hilbert space L_2 and extended by the Carleman rotation by an angle π. As a result, we obtain an efficient criterion for the operators from the indicated C^* -algebra to be Fredholm operators.