On isometric copies of ℓ∞ and James constants in Cesàro–Orlicz sequence spaces

Abstract

For a wide class of Orlicz functions not satisfying the growth condition δ 2 we show that the Cesàro-Orlicz sequence spaces ces ϕ equipped with the Luxemburg norm contain an order linearly isometric copy of ∞ . We also compute the n-th James constant in these spaces for any Orlicz function ϕ, under either the Luxemburg or Orlicz norm, showing that they are equal to n for any natural n 2. In particular, we prove that the non-trivial spaces ces ϕ are not B-convex for any Orlicz function ϕ.