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

For a wide class of Orlicz functions not satisfying the growth condition δ2 we show that the Cesàro–Orlicz sequence spaces cesφ equipped with the Luxemburg norm contain an order linearly isometric copy of ℓ∞. 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 cesφ are not B-convex for any Orlicz function φ.