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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12406 |
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| _version_ | 1866914160086876160 |
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| author | Wang, Di. Li, Yongjin. |
| author_facet | Wang, Di. Li, Yongjin. |
| contents | In this paper, we investigate the extremal structure of the unit ball in the most general classes of Orlicz--Lorentz spaces. the characterizations of extreme points, strongly extreme points, and exposed points are given for Orlicz--Lorentz function spaces $Λ_{φ,ω}$ generated by an arbitrary Orlicz function $φ$ and a non--increasing weight function $ω$, without assuming $φ$ is an $N$-function and $ω$ is strict decreasing. Furthermore, we provide necessary and sufficient conditions for a functional in the dual space to attain its Luxemburg norm at $x \in Λ_{φ,ω}$ without assuming that $φ$ is an $N$--function. The supporting functionals of $x \in Λ_{φ,ω}$ are also characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extreme points, strongly extreme points and exposed points in Orlicz--Lorentz spaces Wang, Di. Li, Yongjin. Functional Analysis In this paper, we investigate the extremal structure of the unit ball in the most general classes of Orlicz--Lorentz spaces. the characterizations of extreme points, strongly extreme points, and exposed points are given for Orlicz--Lorentz function spaces $Λ_{φ,ω}$ generated by an arbitrary Orlicz function $φ$ and a non--increasing weight function $ω$, without assuming $φ$ is an $N$-function and $ω$ is strict decreasing. Furthermore, we provide necessary and sufficient conditions for a functional in the dual space to attain its Luxemburg norm at $x \in Λ_{φ,ω}$ without assuming that $φ$ is an $N$--function. The supporting functionals of $x \in Λ_{φ,ω}$ are also characterized. |
| title | Extreme points, strongly extreme points and exposed points in Orlicz--Lorentz spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.12406 |