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

Let La2 be the Bergman space of the unit disk and I-fraktur sign(La2) be the Banach algebra generated by Toeplitz operators Tf, with f ∈ L∞, We prove that the closed bilateral ideal of I-fraktur sign(La2) generated by operators of the form TfTg - T gTf coincides with I-fraktur sign(La 2).

Guardado en:
Detalles Bibliográficos
Autor principal: Suárez, D.
Formato: JOUR
Materias:
Bergman space
Commutator ideal
Toeplitz operators
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03794024_v51_n1_p105_Suarez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:Let La2 be the Bergman space of the unit disk and I-fraktur sign(La2) be the Banach algebra generated by Toeplitz operators Tf, with f ∈ L∞, We prove that the closed bilateral ideal of I-fraktur sign(La2) generated by operators of the form TfTg - T gTf coincides with I-fraktur sign(La 2).

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