Reflexivity and hyperreflexivity of operator spaces

In this paper, we show that if S is an n-dimensional subspace of L(V ) such that every nonzero transformation of S has rank greater than or equal to 2n − 1 then S is algebraically reflexive. If S is an n-dimensional subspace of B(H) such that every nonzero transformation of S has rank greater than or equal to 2n−1 then S is hyperreflexive. We also consider how to construct some new hyperreflexive subspaces.  2003 Elsevier Science (USA). All rights reserved