Anatomy of the Algebra Generated by Toeplitz Operators with Piece-wise continuous Symbols

Abstract

In this chapter we continue the study of the C^*-algebra generated by Toeplitz operators T _a with piece-wise continuous defining symbols a acting on the Bergman space ($\mathcal{A}^2 \left( \mathbb{D} \right)$) on the unit disk $\mathbb{D}$. Our aim here is to describe explicitly each operator from this algebra and to characterize the Toeplitz operators which belong to the algebra.