  Given a unital C*-subalgebra of B(H), we study the set of all possible images
of its injective envelope that are contained in B(H) and their position
relative to the double commutant of the algebra in order to obtain more
information about the existence or non-existence of weak expectations. We study
the subset of B(H) that is the intersection of all possible images of the
injective envelope and show that it is simultaneously a reflexive cover and a
new type of order completion of the algebra.

Operator Algebras