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# 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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