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

Abstract

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

19 pages, 2 figures

Cited by in corpus (2)

• Radial operators on polyanalytic Bargmann-Segal-Fock spaces
• C*-algebras generated by radial Toeplitz operators on polyanalytic weighted Bergman spaces