Rational Cuntz states peak on the free disk algebra
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911789396000768 |
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| author | Martin, Robert T. W. Shamovich, Eli |
| author_facet | Martin, Robert T. W. Shamovich, Eli |
| contents | We apply realization theory of non-commutative rational multipliers of the Fock space, or free Hardy space of square--summable power series in several non-commuting variables to the convex analysis of states on the Cuntz algebra. We show, in particular, that a large class of Cuntz states which arise as the `non-commutative Clark measures' of isometric NC rational multipliers are peak states for Popescu's free disk algebra in the sense of Clouâtre and Thompson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00508 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational Cuntz states peak on the free disk algebra Martin, Robert T. W. Shamovich, Eli Operator Algebras Functional Analysis We apply realization theory of non-commutative rational multipliers of the Fock space, or free Hardy space of square--summable power series in several non-commuting variables to the convex analysis of states on the Cuntz algebra. We show, in particular, that a large class of Cuntz states which arise as the `non-commutative Clark measures' of isometric NC rational multipliers are peak states for Popescu's free disk algebra in the sense of Clouâtre and Thompson. |
| title | Rational Cuntz states peak on the free disk algebra |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2307.00508 |