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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.05407 |
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| _version_ | 1866910402487517184 |
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| author | Rodríguez, José |
| author_facet | Rodríguez, José |
| contents | Let $ν$ be a vector measure defined on a $σ$-algebra $Σ$ and taking values in a Banach space. We prove that if $ν$ is homogeneous and $L_1(ν)$ is non-separable, then there is a vector measure $\tildeν:Σ\to c_0(κ)$ such that $L_1(ν)=L_1(\tildeν)$ with equal norms, where $κ$ is the density character of $L_1(ν)$. This is a non-separable version of a result of [G.P. Curbera, Pacific J. Math. 162 (1994), no. 2, 287--303]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On vector measures with values in $c_0(κ)$ Rodríguez, José Functional Analysis Let $ν$ be a vector measure defined on a $σ$-algebra $Σ$ and taking values in a Banach space. We prove that if $ν$ is homogeneous and $L_1(ν)$ is non-separable, then there is a vector measure $\tildeν:Σ\to c_0(κ)$ such that $L_1(ν)=L_1(\tildeν)$ with equal norms, where $κ$ is the density character of $L_1(ν)$. This is a non-separable version of a result of [G.P. Curbera, Pacific J. Math. 162 (1994), no. 2, 287--303]. |
| title | On vector measures with values in $c_0(κ)$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.05407 |