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

TL;DR

This paper characterizes the C*-algebra generated by radial Toeplitz operators on the Fock space, showing it is isometrically isomorphic to a C*-algebra of sequences continuous under a square-root metric, with eigenvalues densely spanning this algebra.

Contribution

It establishes an isometric isomorphism between the Toeplitz operator algebra and a sequence algebra based on the square-root metric, linking operator theory with sequence spaces.

Findings

The C*-algebra of radial Toeplitz operators is isometrically isomorphic to a sequence algebra.

Eigenvalues of radial Toeplitz operators are dense in the sequence algebra.

Sequences of eigenvalues are uniformly continuous with respect to the square-root metric.

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