A quantum harmonic analysis approach to the Berger-Coburn theorem
Vishwa Dewage, Mishko Mitkovski
TL;DR
This paper employs quantum harmonic analysis to simplify the proof of the Berger-Coburn theorem concerning Toeplitz operators, and also examines their compactness and Schatten-class properties.
Contribution
It introduces a quantum harmonic analysis approach to streamline proofs and extend understanding of Toeplitz operators' properties.
Findings
Simplified proof of the Berger-Coburn theorem
Analysis of compactness of Toeplitz operators
Investigation of Schatten-class membership
Abstract
We use quantum harmonic analysis for densely defined operators to provide a simplified proof of the Berger-Coburn theorem for boundedness of Toeplitz operators. In addition, we revisit compactness and Schatten-class membership of densely defined Toeplitz operators.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics