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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