Isomorphic ℓp-Subspaces in Orlicz-Lorentz Sequence Spaces

Given a decreasing weight w and an Orlicz function φ satisfying the Δ2-condition at zero, we show that the Orlicz-Lorentz sequence space$d(w, \varphi)$contains an$(1 + \epsilon)$-isomorphic copy of ℓp,$1 \leq p < \infty$, if and only if the Orlicz sequence space$\ell_\varphi$does, that is, if$p \in [\alpha_\varphi, \beta_\varphi]$, where$\alpha_\varphi$and$\beta_\varphi$are the Matuszewska-Orlicz lower and upper indices of φ, respectively. If φ does not satisfy the Δ2-condition, then a similar result holds true for order continuous subspaces$d_0(w, \varphi)$and$h_\varphi$of$d(w, \varphi)$and$\ell_\varphi$, respectively.