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arXiv · 2601.09934

Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra

Joseph C. Várilly·José M. Gracia-Bondía
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Abstract

The topology of the Moyal $*$-algebra may be defined in three ways: the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself; or one may construct the $*$-algebra via a filtration of Hilbert spaces (or other Banach spaces) of distributions. We prove the equivalence of the three topologies thereby obtained. As a consequence, by filtrating the space of tempered distributions by Banach subspaces, we give new sufficient conditions for a phase-space function to correspond to a trace-class operator via the Weyl correspondence rule.

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Joseph C. Várilly, José M. Gracia-Bondía. 2026-01-14. Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra. https://doi.org/10.1063/1.527984

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