The Toeplitz algebra on the Bergman space coincides with its commutator ideal

Abstract

Let L^2-a be the Bergman space of the unit disk and T(L^2_a) be the Banach algebra generated by Toeplitz operators T_f , with f ∈ L∞. We prove that the closed bilateral ideal of T(L2a) generated by operators of the form T_fT_g − T_gT_f coincides with T(L^2_a).Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin