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 $L_{\infty}$-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 $\rho(j,k)=|\sqrt{\vphantom{jk}j}-\sqrt{\vphantom{jk}k}\,|$. More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.