Dixmier trace and the Fock space
Helene Bommier-Hato, Miroslav Englis, El-Hassan Youssfi
TL;DR
This paper establishes criteria for certain operators on the Fock space to belong to the Dixmier class and computes their trace, also extending results to Weyl pseudodifferential operators.
Contribution
It provides new criteria and explicit computations for Dixmier traces of Toeplitz, Hankel, and Weyl operators on the Fock space, advancing operator theory in this context.
Findings
Criteria for Dixmier class membership of operators
Explicit computation of Dixmier traces
Extension of results to Weyl pseudodifferential operators
Abstract
We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal-Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. At the same time, analogous results for the Weyl pseudodifferential operators are also obtained.
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Taxonomy
TopicsHolomorphic and Operator Theory · Spectral Theory in Mathematical Physics · Advanced Algebra and Geometry