We use results and techniques from Werner’s “quantum harmonic analysis” to show that G-invariant Toeplitz operators on \(\mathcal {F}^2\) are norm dense in G-invariant Toeplitz algebras for all subgroups G of the affine unitary group \(U_n\ltimes \mathbb {C}^n\) . Additionally, we prove that the quasi-radial Toeplitz operators are dense in the quasi-radial Toeplitz algebra over the Bergman space \(\mathcal {A}^2\) and prove that G-invariant Toeplitz operators are SOT dense in the algebra of all G-invariant bounded operators on \(\mathcal {F}^2\) .
