# Journal of Operator Theory

Volume 51, Issue 1, Winter 2004 pp. 105-114.

The Toeplitz algebra on the Bergman space coincides with its commutant ideal**Authors**: Daniel Suarez

**Author institution:**Departamento de Matematica, Facultad de Cientas Exactas y Naturales, UBA, Pab. I, Ciudad Universitaria, Nunez, Capital Federal, Argentina

**Summary:**Let $L^2_a$ be the Bergman space of the unit disk and $\toep(L^2_a)$ be the Banach algebra generated by Toeplitz operators $T_f$, with $f\in L^\infty$. We prove that the closed bilateral ideal of $\toep(L^2_a)$ generated by operators of the form $T_f T_g - T_g T_f$ coincides with $\toep(L^2_a)$.

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