A forgotten theorem of Ortyński, not far off

Abstract

We combine techniques of Ortyński \cite{orty} and Moreno and Plichko \cite{moreplic} to show that, for $0<p<\infty$, every subspace of ${\ell }_p(\Gamma )$ having density character $\mathfrak{m}$ has the form ${\ell }_p(\mathfrak{m},H_m)$ for some family of subspaces $H_m\subset {\ell }_p$. The ideas of Ortyński are then applied to obtain unique positions for Lindenstrauss spaces.

arXiv commentThe paper must be withdrawn because it contains a wrong proof