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

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

2012-01-10

arxiv.org/abs/1201.2161v1

Mathematics

Operator Algebras

Scientific paper

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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