The $p$-Operator Approximation Property
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915329549008896 |
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| author | Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel |
| author_facet | Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel |
| contents | We study a notion analogous to the $p$-Approximation Property ($p$-AP) for Banach spaces, within the noncommutative context of operator spaces. Referred to as the $p$-Operator Approximation Property ($p$-OAP), this concept is linked to the ideal of operator $p$-compact mappings. We present several equivalent characterizations based on the density of finite-rank mappings within specific spaces for different topologies, and also one in terms of a slice mapping property. Additionally, we investigate how this property transfers from the dual or bidual to the original space. As an application, the $p$-OAP for the reduced $C^*$-algebra of a discrete group implies that operator $p$-compact Herz-Schur multipliers can be approximated in $\mbox{cb}$-norm by finitely supported multipliers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $p$-Operator Approximation Property Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel Functional Analysis Operator Algebras 47L25, 46B20, 46L05, 46L07 We study a notion analogous to the $p$-Approximation Property ($p$-AP) for Banach spaces, within the noncommutative context of operator spaces. Referred to as the $p$-Operator Approximation Property ($p$-OAP), this concept is linked to the ideal of operator $p$-compact mappings. We present several equivalent characterizations based on the density of finite-rank mappings within specific spaces for different topologies, and also one in terms of a slice mapping property. Additionally, we investigate how this property transfers from the dual or bidual to the original space. As an application, the $p$-OAP for the reduced $C^*$-algebra of a discrete group implies that operator $p$-compact Herz-Schur multipliers can be approximated in $\mbox{cb}$-norm by finitely supported multipliers. |
| title | The $p$-Operator Approximation Property |
| topic | Functional Analysis Operator Algebras 47L25, 46B20, 46L05, 46L07 |
| url | https://arxiv.org/abs/2410.05014 |