Journal of Operator Theory

Volume 93, Issue 2, Spring 2025 pp. 593-620.

Commutative $G$-invariant Toeplitz $C^\ast$-algebras on the Fock space and their Gelfand theory through quantum harmonic analysis

Authors: Robert Fulsche (1), Miguel Angel Rodriguez Rodriguez (2)
Author institution: (1) Institut fuer Analysis, Leibniz Universitaet Hannover, Welfengarten 1, 30167 Hannover, Germany
(2) Institut fuer Analysis, Leibniz Universitaet Hannover, Welfengarten 1, 30167 Hannover, Germany

Summary: We discuss the notion of spectral synthesis for the setting of quantum harmonic analysis. Using these concepts, we study subalgebras of the full Toeplitz algebra with certain invariant symbols and their commutators. In particular, we find a new class of commutative Toeplitz $C^\ast$-algebras on the Fock space. In the end, we investigate the Gelfand theory of those commutative $C^\ast$-algebras.

DOI: http://dx.doi.org/10.7900/jot.2023jul28.2434
Keywords: spectral synthesis, Toeplitz algebras, Fock spaces

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