A note on the strict sigularity of the inclusion between Nakano sequence spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908720166862848 |
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| author | Sanchiz, Mauro |
| author_facet | Sanchiz, Mauro |
| contents | We characterize the strictly singular inclusions $\ell_{p_n}\hookrightarrow\ell_{q_n}$ between Nakano sequence spaces providing a useful criterion, namely $\varliminf_{n\rightarrow\infty}\vert p_n-q_n\vert>0$ (also recently obtained by Lang and Nekvinda in [12] with a different proof). It is also noted that no inclusion operator between Nakano sequence spaces is compact, neither $L$-weakly compact nor $M$-weakly compact. An easy criterion is given for the weak compactness of the inclusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the strict sigularity of the inclusion between Nakano sequence spaces Sanchiz, Mauro Functional Analysis We characterize the strictly singular inclusions $\ell_{p_n}\hookrightarrow\ell_{q_n}$ between Nakano sequence spaces providing a useful criterion, namely $\varliminf_{n\rightarrow\infty}\vert p_n-q_n\vert>0$ (also recently obtained by Lang and Nekvinda in [12] with a different proof). It is also noted that no inclusion operator between Nakano sequence spaces is compact, neither $L$-weakly compact nor $M$-weakly compact. An easy criterion is given for the weak compactness of the inclusion. |
| title | A note on the strict sigularity of the inclusion between Nakano sequence spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.16633 |