Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908767070715904 |
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| author | Várilly, Joseph C. Gracia-Bondía, José M. |
| author_facet | Várilly, Joseph C. Gracia-Bondía, José M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra Várilly, Joseph C. Gracia-Bondía, José M. Operator Algebras Mathematical Physics 46F10 (Primary) 81S30 (Secondary) 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. |
| title | Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra |
| topic | Operator Algebras Mathematical Physics 46F10 (Primary) 81S30 (Secondary) |
| url | https://arxiv.org/abs/2601.09934 |