We consider the generalized Lorentz space Lψ,τ (Tm) defined by some continuous concave function ψ such that ψ(0) = 0. For two spaces Lψ1,τ1 (Tm) and Lψ2,τ2 (Tm) such that αψ1 = limt→0ψ1(2t)/ψ1(t) = βψ2 = limt→0ψ2(2t)/ψ2(t), ...