Existence and characterization of best Φ-approximations by linear subspaces

摘要

Given an Orlicz space L~Φ, we give very relaxed sufficient conditions on Φ to ensure that there exists a best Φ-approximation from any finite dimensional bounded linear subspace S c L~Φ. In addition, given an operator T, defined from L~Φ into itself, we give necessary and sufficient conditions on T to ensure that this is a best Φ-approximation operator from a linear subspace S.