Uniqueness of Hahn-Banach extensions in locally convex spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912717875445760 |
|---|---|
| author | Karak, Sainik Kumar, Akshay Paul, Tanmoy |
| author_facet | Karak, Sainik Kumar, Akshay Paul, Tanmoy |
| contents | We intend to study the uniqueness of the Hahn-Banach extensions of linear functionals on a subspace in locally convex spaces. Various characterizations are derived when a subspace $Y$ has an analogous version of property-U (introduced by Phelps) in a locally convex space, referred to as the property-SNP. We characterize spaces where every subspace has this property. It is demonstrated that a subspace $M$ of a Banach space $E$ has property-U if and only if the subspace $M$ of the locally convex space $E$ endowed with the weak topology has the property-SNP, mentioned above. This investigation circles around exploring the potential connections between the family of seminorms and the unique extension of functionals previously mentioned. We extensively studied this property on the spaces of continuous functions on Tychonoff spaces endowed with the topology of pointwise convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of Hahn-Banach extensions in locally convex spaces Karak, Sainik Kumar, Akshay Paul, Tanmoy Functional Analysis General Topology 46A22, 46A03, 46E10 We intend to study the uniqueness of the Hahn-Banach extensions of linear functionals on a subspace in locally convex spaces. Various characterizations are derived when a subspace $Y$ has an analogous version of property-U (introduced by Phelps) in a locally convex space, referred to as the property-SNP. We characterize spaces where every subspace has this property. It is demonstrated that a subspace $M$ of a Banach space $E$ has property-U if and only if the subspace $M$ of the locally convex space $E$ endowed with the weak topology has the property-SNP, mentioned above. This investigation circles around exploring the potential connections between the family of seminorms and the unique extension of functionals previously mentioned. We extensively studied this property on the spaces of continuous functions on Tychonoff spaces endowed with the topology of pointwise convergence. |
| title | Uniqueness of Hahn-Banach extensions in locally convex spaces |
| topic | Functional Analysis General Topology 46A22, 46A03, 46E10 |
| url | https://arxiv.org/abs/2504.18947 |