Toeplitz Operators on the Fock Space with Quasi-Radial Symbols

Authors

Vishwa Dewage, Louisiana State University
Gestur Ólafsson, Louisiana State University

Document Type

Article

Publication Date

6-1-2022

Abstract

The Fock space F(Cⁿ) is the space of holomorphic functions on Cⁿ that are square-integrable with respect to the Gaussian measure on Cⁿ. This space plays an important role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Esmeral and Maximenko showed in 2016 that radial Toeplitz operators on F(C) generate a commutative C^∗-algebra which is isometrically isomorphic to the C^∗-algebra Cb,u(N, ρ1). In this article, we extend the result to k-quasi-radial symbols acting on the Fock space F(Cⁿ). We calculate the spectra of the said Toeplitz operators and show that the set of all eigenvalue functions is dense in the C^∗-algebra Cb,u(N0k,ρk) of bounded functions on N0k which are uniformly continuous with respect to the square-root metric. In fact, the C^∗-algebra generated by Toeplitz operators with quasi-radial symbols is Cb,u(N0k,ρk).

Publication Source (Journal or Book title)

Complex Analysis and Operator Theory

Recommended Citation

Dewage, V., & Ólafsson, G. (2022). Toeplitz Operators on the Fock Space with Quasi-Radial Symbols. Complex Analysis and Operator Theory, 16 (4) https://doi.org/10.1007/s11785-022-01208-9