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arXiv · 1201.2161

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

Raul Quiroga-Barranco·Armando Sanchez-Nungaray
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Abstract

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 $\mathbb{P}^n(\mathbb{C})$. The latter is also proved for the corresponding symbols and algebras on $\mathbb{B}^n$.

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Raul Quiroga-Barranco, Armando Sanchez-Nungaray. 2014-04-03. Toeplitz operators with quasi-radial quasi-homogeneous symbols and bundles of Lagrangian frames. https://arxiv.org/abs/1201.2161

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