Operators on injective tensor products of separable Banach spaces and spaces with few operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909798068387840 |
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| author | Acuaviva, Antonio |
| author_facet | Acuaviva, Antonio |
| contents | We give a characterization of the operators on the injective tensor product $E \hat{\otimes}_\varepsilon X$ for any separable Banach space $E$ and any (non-separable) Banach space $X$ with few operators, in the sense that any operator $T: X \to X$ takes the form $T = λI + S$ for a scalar $λ\in \mathbb{K}$ and an operator $S$ with separable range. This is used to give a classification of the complemented subspaces and closed operator ideals of spaces of the form $C_0(ω\times K_\mathcal{A})$, where $K_\mathcal{A}$ is a locally compact Hausdorff space induced by an almost disjoint family $\mathcal{A}$ such that $C_0(K_\mathcal{A})$ has few operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operators on injective tensor products of separable Banach spaces and spaces with few operators Acuaviva, Antonio Functional Analysis 46B26, 47L10, 46B20, 46M05 (Primary) 46E15, 54G12, 54B10 (Secondary) We give a characterization of the operators on the injective tensor product $E \hat{\otimes}_\varepsilon X$ for any separable Banach space $E$ and any (non-separable) Banach space $X$ with few operators, in the sense that any operator $T: X \to X$ takes the form $T = λI + S$ for a scalar $λ\in \mathbb{K}$ and an operator $S$ with separable range. This is used to give a classification of the complemented subspaces and closed operator ideals of spaces of the form $C_0(ω\times K_\mathcal{A})$, where $K_\mathcal{A}$ is a locally compact Hausdorff space induced by an almost disjoint family $\mathcal{A}$ such that $C_0(K_\mathcal{A})$ has few operators. |
| title | Operators on injective tensor products of separable Banach spaces and spaces with few operators |
| topic | Functional Analysis 46B26, 47L10, 46B20, 46M05 (Primary) 46E15, 54G12, 54B10 (Secondary) |
| url | https://arxiv.org/abs/2503.21379 |