Algebras Generated by the Bergman Projection and Operators of Multiplication by Piecewise Continuous Functions

Let D be the unit disk. For A (subset of) L (infinity) (D) containing piecewise continuous functions, we study the C*algebras R(A) generated by the Bergman projection for D and operators of multiplication by functions of A .These algebras are related to the algebra generated by more than two projections depending on how many limits a function has at a boundary point. We find the description of the symbol algebra of R(A), denoted here by R(A). Interesting facts about representations of R(A) are found and we construct a special family of coefficients such that the algebra R(A) has irreducible representations of predefined dimensions.