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

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 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 ces φ are not B-convex for any Orlicz function φ.