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.