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 δ, 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. © 2010 Elsevier Inc.

Publication Title

Journal of Mathematical Analysis and Applications