On the C (*)-Algebra Generated by the Bergman Operator, Carleman Second-Order Shift, and Piecewise Continuous Coefficients

摘要

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 pi. As a result, we obtain an efficient criterion for the operators from the indicated C (*) -algebra to be Fredholm operators.