On Opial properties and Opial modulus for Orlicz sequence spaces Original Research Article

Criteria in order that a Orlicz sequence space lΦ (or its subspace hΦ) has the Opial property, the locally uniform Opial property and the uniform Opial property are given for the Luxemburg norm. For the Orlicz norm only criteria for the positive Opial property and for the uniform Opial property are presented. Formulae for the Opial modulus in lΦ are obtained for both norms. In consequence, Opial modulus is calculated for lΦ generated by Φ(u)=up(1⩽p<∞) and Φ(u)=u2+u4.