On weak uniform normal structure in weighted Orlicz sequence spaces

It is proved that a weighted Orlicz sequence space M(w), equipped with Luxemburg or Amemiya norm has weak uniform normal structure iff M(w) ∼= hM(w) for wide class of weight sequences w = {wn}∞ n=1. An example is constructed, where M has not Δ2-condition but by choosing a suitable weight sequence limn→∞wn=∞we get that M(w) has weak uniform normal structure. © 2007 Elsevier Inc. All rights reserved