On \(\ell^ p\)-copies in Musielak-Orlicz sequence spaces
We study \(\ell^ p\)-copies in Musielak-Orlicz sequence spaces \(\ell^ M\) also called modular sequence spaces. We present a necessary condition on the function \(x^ p\) in order that \(\ell^ p\) can be isomorphic to a subspace of a Musielak-Orlicz sequence space \(\ell^ M\). As application, we characterize the \(\ell^ p\)-copies in Nakano sequence spaces \(\ell^{(p_ n)}\). Namely, if \(0<\inf_{n}\{p_ n)\leq \sup_{n}\{p_ n\}<\infty\), then \(\ell^ p\) is isomorphic to a (complemented) subspace of \(\ell^ p\) if and only if p is an accumulation point of \((p_ n)^{\infty}_{n=1}\).
\(\ell ^ p\)-copies in Musielak-Orlicz sequence spaces \(\ell ^ M\)
scientific article; zbMATH DE number 4203053