Isomorphic ℓ p-subspaces in orlicz-lorentz sequence spaces


Given a decreasing weight w and an Orlicz function φ satisfying the Δ 2-condition at zero, we show that the Orlicz-Lorentz sequence space d(w,φ) contains an (1 + ε)-isomorphic copy of ℓ p, 1 ≤ p < ∞, if and only if the Orlicz sequence space ℓ φ does, that is, if p ∈ [α φ, β φ], where α φ, and β φ are the Matuszewska-Orlicz lower and upper indices of φ, respectively. If φ does not satisfy the Δ 2-condition, then a similar result holds true for order continuous subspaces d 0(w, φ) and hφ of d(w, φ) and ℓ φ, respectively. © 2006 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society