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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 199-222.

Toeplitz operators with quasi-radial quasi-homogeneous symbols and bundles of Lagrangian frames

Authors: Raul Quiroga-Barranco (1) and Armando Sanchez-Nungaray (2)
Author institution: (1) Centro de Investigacion en Matematicas, Guanajuato, Mexico
(2) Centro de Investigacion en Matematicas, Guanajuato, Mexico and Facultad de Matematicas, Universidad Veracruzana, Veracruz, Mexico

Summary:  We prove that the quasi-homogenous symbols on the projective space $\mathbb{P}^n(\mathbb{C})$ yield commutative algebras of Toeplitz operators on all weighted Bergman spaces, thus extending to this compact case known results for the unit ball $\mathbb{B}^n$. These algebras are Banach but not $C^*$. We prove the existence of a strong link between such symbols and algebras with the geometry of $\mathbb{P}^n(\mathbb{C})$.

Keywords:  Toeplitz operators, commutative Banach algebras, Lagrangian frames, complex projective space.

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