Linearizing holomorphic functions on operator spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909203011993600 |
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| author | Chávez-Domínguez, Javier Alejandro Dimant, Verónica |
| author_facet | Chávez-Domínguez, Javier Alejandro Dimant, Verónica |
| contents | We introduce a notion of completely bounded holomorphic functions defined on the open unit ball of an operator space. We endow the set of these functions with an operator space structure, and in the scalar-valued case we identify an operator space predual for it which is a noncommutative version of Mujica's predual for the space of bounded holomorphic functions and satisfies similar properties. In particular, our predual is a free holomorphic operator space in the sense that it satisfies a linearization property for vector-valued completely bounded holomorphic functions. Additionally, several different operator space approximation properties transfer between the predual and the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linearizing holomorphic functions on operator spaces Chávez-Domínguez, Javier Alejandro Dimant, Verónica Functional Analysis Complex Variables Operator Algebras 46G20, 46T25, 47L25, 46L07 We introduce a notion of completely bounded holomorphic functions defined on the open unit ball of an operator space. We endow the set of these functions with an operator space structure, and in the scalar-valued case we identify an operator space predual for it which is a noncommutative version of Mujica's predual for the space of bounded holomorphic functions and satisfies similar properties. In particular, our predual is a free holomorphic operator space in the sense that it satisfies a linearization property for vector-valued completely bounded holomorphic functions. Additionally, several different operator space approximation properties transfer between the predual and the domain. |
| title | Linearizing holomorphic functions on operator spaces |
| topic | Functional Analysis Complex Variables Operator Algebras 46G20, 46T25, 47L25, 46L07 |
| url | https://arxiv.org/abs/2405.08826 |