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Powers and roots of Toeplitz operators

Authors:	Issam Louhichi

Affiliation:	UFR Mathématiques et Informatique, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France

Abstract:	We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in $L^{infty}(mathbb{D})$ which commute with Toeplitz operators whose symbols are of the form $e^{iptheta}r^m$ .

Keywords:	Toeplitz operators Bergman space Mellin transform.

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