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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2407.19925 |
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| _version_ | 1866910545634918400 |
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| author | Chen, Deliang |
| author_facet | Chen, Deliang |
| contents | The Machado--Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado's distance formula for bounded weighted vector-valued functions. A number of applications are given; in particular, some types of the Bishop--Stone--Weierstrass theorem for bounded vector-valued continuous spaces in the uniform topology are discussed; the splitting of $C(I \times J, X \otimes Y)$ as the closure of $C(I, X) \otimes C(J, Y)$ in different senses and the extension of continuous vector-valued functions are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Machado--Bishop theorem in the uniform topology Chen, Deliang Functional Analysis Classical Analysis and ODEs Primary 41A65, Secondary 46E40, 54C20, 46M05 The Machado--Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado's distance formula for bounded weighted vector-valued functions. A number of applications are given; in particular, some types of the Bishop--Stone--Weierstrass theorem for bounded vector-valued continuous spaces in the uniform topology are discussed; the splitting of $C(I \times J, X \otimes Y)$ as the closure of $C(I, X) \otimes C(J, Y)$ in different senses and the extension of continuous vector-valued functions are studied. |
| title | The Machado--Bishop theorem in the uniform topology |
| topic | Functional Analysis Classical Analysis and ODEs Primary 41A65, Secondary 46E40, 54C20, 46M05 |
| url | https://arxiv.org/abs/2407.19925 |