On \(\ell ^ p\)-complemented copies in Orlicz spaces
Let \(1\leq \alpha \leq \beta <\infty\) and let F be a closed subset of [\(\alpha\),\(\beta\) ]. If \(\alpha >1\) (resp. \(\alpha =1)\), then there is an Orlicz sequence space \(\ell^{\phi}\) with indices \(\alpha_{\phi}=\alpha\) and \(\beta_{\phi}=\beta\) which contains a complemented copy of \(\ell^ p\) if and only if \(p\in F\) (resp. \(p\in F\cup \{1\})\). Similar results remain true also for Orlicz function spaces. A recent result of the first author and \textit{V. Peirats} [Isr. J. Math. 56, 355-360 (1986; Zbl 0631.46030)] concerning the existence of a minimal Orlicz space \(L^{\phi}(\mu)\) with no complemented copy of \(\ell^ p\) for any \(p\neq 2\) is proved.
scientific article; zbMATH DE number 4078002
scientific article