Work

Commutative C$$^*$$ algebras and Gelfand theory through phase space methods

Year: 2025

Type: article

Abstract: We show how the Gelfand spectrum of certain commutative operator algebras can be studied based on the theorem of Stone and von Neumann. The method presented is a natural addition to the tools of quantum spectral synthesis , which were recently used to characterize certain commutative Toeplitz algebras on the Fock space. Our method applies to this setting and also to more general abelian phase spaces. Besides characterizing Gelfand spectra of such commutative operator algebras, we also prove an extension of this result to the operator-valued case.

Source: Boletín de la Sociedad Matemática Mexicana

DOI: 10.1007/s40590-025-00806-9

Authors: Robert Fulsche, Oliver Fürst

Institutions: Leibniz University Hannover, University of Bonn

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Gottfried Wilhelm Leibniz Universität Hannover