1-Hyperreflexivity and Complete Hyperreflexivity

The subspaces and subalgebras of B(H) which are hyperreflexive with constant 1 are completely classified. It is shown that there are 1-hyperreflexive subspaces for which the complete hyperreflexivity constant is strictly greater than 1. The constants for \bC T \otimes B(H) are analyzed in detail.Comment: 41 page