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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23063 |
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| _version_ | 1866909372452438016 |
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| author | Aubrun, Guillaume Müller-Hermes, Alexander |
| author_facet | Aubrun, Guillaume Müller-Hermes, Alexander |
| contents | Given an operator $ϕ:X\rightarrow Y$ between Banach spaces, we consider its tensor powers $ϕ^{\otimes k}$ as operators from the $k$-fold injective tensor product of $X$ to the $k$-fold projective tensor product of $Y$. We show that after taking the $k$th root, the operator norm of $ϕ^{\otimes k}$ converges to the $2$-dominated norm $γ^*_2(ϕ)$, one of the standard operator ideal norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit formulas for norms of tensor power operators Aubrun, Guillaume Müller-Hermes, Alexander Functional Analysis Quantum Physics Given an operator $ϕ:X\rightarrow Y$ between Banach spaces, we consider its tensor powers $ϕ^{\otimes k}$ as operators from the $k$-fold injective tensor product of $X$ to the $k$-fold projective tensor product of $Y$. We show that after taking the $k$th root, the operator norm of $ϕ^{\otimes k}$ converges to the $2$-dominated norm $γ^*_2(ϕ)$, one of the standard operator ideal norms. |
| title | Limit formulas for norms of tensor power operators |
| topic | Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2410.23063 |