2022/04/23 by Ruf, Thomas
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2204.12282
For a measure space Ω we extend the theory of Orlicz spaces generated by an even convex integrand φ\colon Ω× X → [ 0, ∞ ] to the case when the range Banach space X is arbitrary. Besides settling fundamental structural properties such as completeness, we characterize separability, reflexivity and represent the dual space. This representation includes the cases when X' has no Radon-Nikodym property or φ is unbounded. We apply our theory to represent convex conjugates and Fenchel-Moreau subdifferentials of integral functionals, leading to the first general such result on function spaces with non-separable range space. For this, we prove a new interchange criterion between infimum and integral for non-separable range spaces, which we consider of independent interest.