Optimal upper and lower sequence spaces with applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912964588601344 |
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| author | Astashkin, Sergey V. Nilsson, Per G. |
| author_facet | Astashkin, Sergey V. Nilsson, Per G. |
| contents | We study the optimal upper $X_U$ and lower $X_L$ sequence spaces that can be assigned to each Banach lattice $X$. These spaces are symmetric, have the Fatou property and the unit vector basis has in these spaces very special properties. Determined by the order structure of $X$ the spaces $X_U$ and $X_L$ turn out to be very useful when studying Banach lattices. Among other results, in terms of these constructions, we identify Banach lattices that satisfy equal-norm upper and lower $p$-estimates, give a characterization of $L_p(μ)$-spaces, derive some properties of the tensor product operator in Lorentz and Orlicz spaces, identify Orlicz spaces in which the unit vector basis is upper (resp. lower) semi-homogeneous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal upper and lower sequence spaces with applications Astashkin, Sergey V. Nilsson, Per G. Functional Analysis Primary 46B42, Secondary 46A45, 46B20 We study the optimal upper $X_U$ and lower $X_L$ sequence spaces that can be assigned to each Banach lattice $X$. These spaces are symmetric, have the Fatou property and the unit vector basis has in these spaces very special properties. Determined by the order structure of $X$ the spaces $X_U$ and $X_L$ turn out to be very useful when studying Banach lattices. Among other results, in terms of these constructions, we identify Banach lattices that satisfy equal-norm upper and lower $p$-estimates, give a characterization of $L_p(μ)$-spaces, derive some properties of the tensor product operator in Lorentz and Orlicz spaces, identify Orlicz spaces in which the unit vector basis is upper (resp. lower) semi-homogeneous. |
| title | Optimal upper and lower sequence spaces with applications |
| topic | Functional Analysis Primary 46B42, Secondary 46A45, 46B20 |
| url | https://arxiv.org/abs/2603.12650 |