  We study operator spaces, operator algebras, and operator modules, from the
point of view of the `noncommutative Shilov boundary'. In this attempt to
utilize some `noncommutative Choquet theory', we find that Hilbert
C$^*-$modules and their properties, which we studied earlier in the operator
space framework, replace certain topological tools. We introduce certain
multiplier operator algebras and C$^*-$algebras of an operator space, which
generalize the algebras of adjointable operators on a C$^*-$module, and the
`imprimitivity C$^*-$algebra'. It also generalizes a classical Banach space
notion. This multiplier algebra plays a key role here. As applications of this
perspective, we unify, and strengthen several theorems characterizing operator
algebras and modules, in a way that seems to give more information than other
current proofs. We also include some general notes on the `commutative case' of
some of the topics we discuss, coming in part from joint work with Christian Le
Merdy, about `function modules'.
