Some properties of prereflexive subspaces of operators

Abstract

In the paper, we define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if S⫅L(H) is prereflexive, then every σ-weakly closed subspace of S is prereflexive if and only if S has the property WP(see definition 2.11). By our result, we construct a reflexive operator A such that A⊕0 is not prereflexive.