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.
Categories: math.FA