Radial Toeplitz operators on the Fock space and square-root-slowly oscillating sequences

In this paper we show that the C*-algebra generated by radial Toeplitz operators with $L_{\mathrm{\infty }}$-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric $\rho (j,k)=\mathrm{\mid }\sqrt{\phantom{jk}j}-\sqrt{\phantom{jk}k}\mathrm{\mid }$. More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.