Grothendieck and ℓ∞‐Grothendieck Subspaces of ℓ∞

ABSTRACT Let . We prove that contains pairwise non‐isomorphic non‐reflexive Grothendieck subspaces. They may all be chosen to contain the canonical copy of and to have an infinite‐dimensional reflexive quotient. This is optimal and answers Problem 24 of González and Kania [ Japanese Journal of Mathematics 16 (2021), 247–313]. We also show that the relative ‐Grothendieck property depends on the specified copy of and is not an isomorphic invariant of the subspace. More generally, for every closed there is an ‐Grothendieck subspace isomorphic to ; taking answers Problem 1 of González et al. [ Journal of Mathematical Analysis and Applications 497 (2021), Article 124857].