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Separately radial and radial Toeplitz operators on the projective space and representation theory

Raul Quiroga-Barranco; Armando Sanchez-Nungaray — 2017

Czechoslovak Mathematical Journal

We consider separately radial (with corresponding group $𝕋^{n}$ ) and radial (with corresponding group $U (n))$ symbols on the projective space $ℙ^{n} (ℂ)$ , as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^{*}$ -algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...

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