Orlicz function spaces without complemented copies of \(\ell ^ p\)
The existence of reflexive Orlicz sequence spaces \(\ell^{\phi}\) containing no complemented subspaces isomorphic to \(\ell^ n\)-space for any \(1\leq p<\infty\) was proved by \textit{J. Lindenstrauss} and \textit{L. Tzafriri} [Isr. J. Math. 11, 355-379 (1972; Zbl 0237.46034) and 14, 368- 389 (1973; Zbl 0262.46031), see also ``Classical Banach spaces I. Sequence spaces.'' (1977; Zbl 0362.46013)]. In this paper we give the corresponding result for Orlicz function spaces \(L^{\phi}[0,1]\). After introducing and studying the class of minimal Orlicz function spaces \(L^{\phi}[0,1]\) we prove the existence of reflexive Orlicz function spaces \(L^{\phi}[0,1]\) that contain no complemented subspaces isomorphic to \(\ell^ p\)-space for any \(1\leq p\neq 2<\infty\).
scientific article; zbMATH DE number 4026115