Some properties of prereflexive subspaces of operators (Q1392710)

Summary: We define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if \({\mathcal S}\subseteq L(H)\) is prereflexive, then every \(\sigma\)-weakly closed subspace of \({\mathcal S}\) is prereflexive if and only if \({\mathcal S}\) has the property WP. By our result, we construct a reflexive operator \(A\) such that \(A\oplus 0\) is not prereflexive.