Abstract
It is proved that a weighted Orlicz sequence space ℓ M ( w ) , equipped with Luxemburg or Amemiya norm has weak uniform normal structure iff ℓ M ( w ) ≅ h M ( w ) for wide class of weight sequences w = { w n } n = 1 ∞ . An example is constructed, where M has not Δ 2 -condition but by choosing a suitable weight sequence lim n → ∞ w n = ∞ we get that ℓ M ( w ) has weak uniform normal structure.
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