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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2509.08921 |
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| _version_ | 1866914031786262528 |
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| author | Karoobi, Ali Martin, Robert T. W. Tornes, Maximilian |
| author_facet | Karoobi, Ali Martin, Robert T. W. Tornes, Maximilian |
| contents | We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre realization about any matrix tuple, $Y$, in its domain, if and only if it is a uniformly analytic non-commutative function defined in a uniformly open neighbourhood of $Y$. This extends the finite-dimensional realization theory of non-commutative rational functions maximally -- to all uniformly analytic non-commutative functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator realizations about a matrix-centre Karoobi, Ali Martin, Robert T. W. Tornes, Maximilian Functional Analysis We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre realization about any matrix tuple, $Y$, in its domain, if and only if it is a uniformly analytic non-commutative function defined in a uniformly open neighbourhood of $Y$. This extends the finite-dimensional realization theory of non-commutative rational functions maximally -- to all uniformly analytic non-commutative functions. |
| title | Operator realizations about a matrix-centre |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.08921 |