An extension of Phelps theorem to spaces of vector-valued functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911581340696576 |
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| author | Dwivedi, Saurabh |
| author_facet | Dwivedi, Saurabh |
| contents | In this paper, our main aim is to extend a classical theorem of Phelps on norm-attaining functionals from the space of scalar-valued continuous functions $C(Ω)$ to its vector-valued counterpart $C(Ω, X)$. One of our main results provides a complete characterization of norm-attaining functionals on $C(Ω, X)$ under the assumption that $X^*$ has the Radon-Nikodým property (RNP). For a general Banach space $X$, we further investigate norm attainment at points of weak$^*$-to-weak continuity for the identity map $Id : (C(Ω, X)_1^*, w^*) \to (C(Ω, X)_1^*, w)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_09133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An extension of Phelps theorem to spaces of vector-valued functions Dwivedi, Saurabh Functional Analysis Primary 46A22, 46B10, 46B25, Secondary 46B20, 46B22 In this paper, our main aim is to extend a classical theorem of Phelps on norm-attaining functionals from the space of scalar-valued continuous functions $C(Ω)$ to its vector-valued counterpart $C(Ω, X)$. One of our main results provides a complete characterization of norm-attaining functionals on $C(Ω, X)$ under the assumption that $X^*$ has the Radon-Nikodým property (RNP). For a general Banach space $X$, we further investigate norm attainment at points of weak$^*$-to-weak continuity for the identity map $Id : (C(Ω, X)_1^*, w^*) \to (C(Ω, X)_1^*, w)$. |
| title | An extension of Phelps theorem to spaces of vector-valued functions |
| topic | Functional Analysis Primary 46A22, 46B10, 46B25, Secondary 46B20, 46B22 |
| url | https://arxiv.org/abs/2604.09133 |