Separating vectors and reflexivity
Let \(V\) be a vector space over a field \(F\), and let \(S\) be a subspace of the space of all linear transformations on \(V\). A vector \(x\in V\) is said to separate \(S\) in case the map sending \(s\) to \(sx\) is injective for all \(s\in S\). This present paper clarifies the connection between separating vectors and reflexivity. The main result of the paper gives conditions under which the existence of separating vectors for a subspace implies that the subspace is algebraically reflexive.
scientific article; zbMATH DE number 69518
scientific article