में बचाया:
| मुख्य लेखक: | |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2026
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2604.14068 |
| टैग: |
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| _version_ | 1866908966953418752 |
|---|---|
| author | Dwivedi, S. |
| author_facet | Dwivedi, S. |
| contents | In this paper, we study non-reflexive Banach spaces $X$ for which the quotient space $X^{**}/X$ is reflexive. Such spaces were first introduced by James R.~Clark, where they were called coreflexive spaces. We show that a space $X$ is coreflexive if and only if every separable subspace $Y\subseteq X$ is coreflexive, provided that $X$ is w$^*$-sequently dense in its bidual $X^{**}$. We show that coreflexive spaces are stable under $\ell^{p}$-sum for $1<p<\infty$. We show that if $X$ is a coreflexive space such that $X^{**}/X$ is separable, then the space of Bochner $p$-integrable functions, $L^{p}(μ,X)$ is coreflexive for $1<p<\infty$. We conclude by providing an alternative proof of the fact, in a quasi-reflexive space $X$, w-PC's of the unit ball $X_{1}$ continue to have the same property in all the higher even-order dual unit balls of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A study on coreflexive Banach Spaces Dwivedi, S. Functional Analysis Primary 46A22, 46B10, 46B25, Secondary 46B20, 46B22 In this paper, we study non-reflexive Banach spaces $X$ for which the quotient space $X^{**}/X$ is reflexive. Such spaces were first introduced by James R.~Clark, where they were called coreflexive spaces. We show that a space $X$ is coreflexive if and only if every separable subspace $Y\subseteq X$ is coreflexive, provided that $X$ is w$^*$-sequently dense in its bidual $X^{**}$. We show that coreflexive spaces are stable under $\ell^{p}$-sum for $1<p<\infty$. We show that if $X$ is a coreflexive space such that $X^{**}/X$ is separable, then the space of Bochner $p$-integrable functions, $L^{p}(μ,X)$ is coreflexive for $1<p<\infty$. We conclude by providing an alternative proof of the fact, in a quasi-reflexive space $X$, w-PC's of the unit ball $X_{1}$ continue to have the same property in all the higher even-order dual unit balls of $X$. |
| title | A study on coreflexive Banach Spaces |
| topic | Functional Analysis Primary 46A22, 46B10, 46B25, Secondary 46B20, 46B22 |
| url | https://arxiv.org/abs/2604.14068 |