On Köthe duals of Orlicz-Lorentz spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929310684676096 |
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| author | Kamińska, Anna Tag, Hyung-Joon |
| author_facet | Kamińska, Anna Tag, Hyung-Joon |
| contents | In this article, we study a number of properties of the Köthe duals $\mathcal{M}_{φ,w}$ of Orlicz-Lorentz spaces. An explicit description of the order-continuous subspace of $\mathcal{M}_{φ,w}$ is provided. Moreover, the separability of these spaces is characterized by the growth condition $Δ_2$. Consequently, the Köthe dual space $\mathcal{M}_{φ,w}$ has the Radon-Nikodým property if and only if the N-function at infinity $φ$ satisfies the appropriate $Δ_2$-condition. The comparison between $\mathcal{M}_{φ,w}$ spaces is characterized via standard orders between Orlicz functions. As applications of these results, we provide sufficient conditions for M-embedded order-continuous subspaces of Orlicz-Lorentz spaces equipped with the Luxemburg norm and prove the existence of a unique norm-preserving extension on Orlicz-Lorentz spaces equipped with the Orlicz norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Köthe duals of Orlicz-Lorentz spaces Kamińska, Anna Tag, Hyung-Joon Functional Analysis In this article, we study a number of properties of the Köthe duals $\mathcal{M}_{φ,w}$ of Orlicz-Lorentz spaces. An explicit description of the order-continuous subspace of $\mathcal{M}_{φ,w}$ is provided. Moreover, the separability of these spaces is characterized by the growth condition $Δ_2$. Consequently, the Köthe dual space $\mathcal{M}_{φ,w}$ has the Radon-Nikodým property if and only if the N-function at infinity $φ$ satisfies the appropriate $Δ_2$-condition. The comparison between $\mathcal{M}_{φ,w}$ spaces is characterized via standard orders between Orlicz functions. As applications of these results, we provide sufficient conditions for M-embedded order-continuous subspaces of Orlicz-Lorentz spaces equipped with the Luxemburg norm and prove the existence of a unique norm-preserving extension on Orlicz-Lorentz spaces equipped with the Orlicz norm. |
| title | On Köthe duals of Orlicz-Lorentz spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.07368 |