Some Geometric Properties in Orlicz Sequence Spaces Equipped with Orlicz Norm

It is proved that for any reflexive Banach space X, both X and $X^*$ are CLUR if and only if both X and $X^*$ have property H. Criteria for rotundity, local uniform rotundity, compact local uniform rotundity and property H in Orlicz sequence spaces equipped with the Orlicz norm are given. Criteria for property H, rotundity and LUR were already known in the literature only for finitely valued Orlicz functions which vanish only at zero and are N-functions (i.e. they satisfy conditions (0₁) and (∞₁). All our criteria except Corollary 2.15 are given for arbitrary Orlicz functions. Criteria for smoothness of $l^0_\Phi$ in Corollary 2.15 are given for any finitely valued Orlicz function satisfying condition (∞₁), extending the respective result of Chen, Hudzik and Wisla proved only for Orlicz functions vanishing only at zero.