Drop properties and approximative compactness in Orlicz–Bochner function spaces

Abstract

The representation of dual spaces of E M ( μ , X ) , owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of L M ( μ , X ) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82–89]. Simultaneously, under some conditions, the weak ∗ drop property in L M ( μ , X ∗ ) and L M ( μ , X ) ∗ is discussed.