adj. 1. (of a relation) holding between any member of the domain and itself. For example,... is a member of the same family as... is reflexive since everyone is a member of his or her own family. Compare irreflexive, non-reflexive. See also equivalence relation. 2. (of a normed space) canonically identifiable with its second normed dual space, possessing a unit ball that is weakly compact. Compare non-reflexive. See also James' theorem.