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arXiv · 2512.16633

A note on the strict sigularity of the inclusion between Nakano sequence spaces

Mauro Sanchiz
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Abstract

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.

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Mauro Sanchiz. 2025-12-18. A note on the strict sigularity of the inclusion between Nakano sequence spaces. https://arxiv.org/abs/2512.16633

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