On various diametral notions of points in the unit ball of some vector-valued function spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929530058309632 |
|---|---|
| author | Lee, Han Ju Roldán, Óscar Tag, Hyung-Joon |
| author_facet | Lee, Han Ju Roldán, Óscar Tag, Hyung-Joon |
| contents | In this article, we study the ccs-Daugavet, ccs-$Δ$, super-Daugavet, super-$Δ$, Daugavet, $Δ$, and $\nabla$ points in the unit balls of vector-valued function spaces $C_0(L, X)$, $A(K, X)$, $L_\infty(μ, X)$, and $L_1(μ, X)$. To partially or fully characterize these diametral points, we first provide improvements of several stability results under $\oplus_\infty$ and $\oplus_1$-sums shown in the literature. For complex Banach spaces, $\nabla$ points are identical to Daugavet points, and so the study of $\nabla$ points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for $L_\infty(μ)$ and uniform algebra when $K$ is infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On various diametral notions of points in the unit ball of some vector-valued function spaces Lee, Han Ju Roldán, Óscar Tag, Hyung-Joon Functional Analysis Primary 46B20, Secondary 46B04, 46E40, 46J10 In this article, we study the ccs-Daugavet, ccs-$Δ$, super-Daugavet, super-$Δ$, Daugavet, $Δ$, and $\nabla$ points in the unit balls of vector-valued function spaces $C_0(L, X)$, $A(K, X)$, $L_\infty(μ, X)$, and $L_1(μ, X)$. To partially or fully characterize these diametral points, we first provide improvements of several stability results under $\oplus_\infty$ and $\oplus_1$-sums shown in the literature. For complex Banach spaces, $\nabla$ points are identical to Daugavet points, and so the study of $\nabla$ points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for $L_\infty(μ)$ and uniform algebra when $K$ is infinite. |
| title | On various diametral notions of points in the unit ball of some vector-valued function spaces |
| topic | Functional Analysis Primary 46B20, Secondary 46B04, 46E40, 46J10 |
| url | https://arxiv.org/abs/2410.04706 |