  We generalize some technical results of Glicksberg to the realm of general
operator algebras and use them to give a characterization of open and closed
projections in terms of certain multiplier algebras. This generalizes a theorem
of J. Wells characterizing an important class of ideals in uniform algebras.
The difficult implication in our main theorem is that if a projection is open
in an operator algebra, then the multiplier algebra of the associated
hereditary subalgebra arises as the closure of the subalgebra with respect to
the strict topology of the multiplier algebra of a naturally associated
hereditary C*-subalgebra. This immediately implies that the multiplier algebra
of an operator algebra A may be obtained as the strict closure of A in the
multiplier algebra of the C*-algebra generated by A.
