## Breitner Ocampo (Vol. 19 No. 1 2015)

Toeplitz operators with piecewise quasicontinuous symbols

Breitner Ocampo

For a fixed subset of the unit circle , , we define the algebra P C of piecewise continuous functions in
with one sided limits at each point . Besides, we let stands for the  -algebra of quasicontinuous functions on
defined by D. Sarason in [5]. We define then as the -algebra generated by and .

stands for the Bergman space of the unit disk , that is, the space of square integrable and analytic functions defined on . Our goal is to describe , the algebra generated by Toeplitz operators whose symbols are certain extensions of functions in
acting on . Of course, a function defined on can be extended to the disk in many ways. The more natural extensions are the harmonic and the radial ones. In the paper we describe the algebra and we prove that this description does not depend on the extension chosen.

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