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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.10545 |
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| _version_ | 1866915109699321856 |
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| author | Bagarello, Fabio Inoue, Hiroshi Triolo, Salvatore |
| author_facet | Bagarello, Fabio Inoue, Hiroshi Triolo, Salvatore |
| contents | We consider a particular class of sesquilinear forms on a {Banach quasi *-algebra} $(\A[\|.\|],\Ao[\|.\|_0])$ which we call {\em eigenstates of an element} $a\in\A$, and we deduce some of their properties. We further apply our definition to a family of ladder elements, i.e. elements of $\A$ obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via GNS-representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements Bagarello, Fabio Inoue, Hiroshi Triolo, Salvatore Mathematical Physics Operator Algebras We consider a particular class of sesquilinear forms on a {Banach quasi *-algebra} $(\A[\|.\|],\Ao[\|.\|_0])$ which we call {\em eigenstates of an element} $a\in\A$, and we deduce some of their properties. We further apply our definition to a family of ladder elements, i.e. elements of $\A$ obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via GNS-representation. |
| title | Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements |
| topic | Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2501.10545 |