On function and operator modules

Let $A$ be a unital Banach algebra. We give a characterization of the left Banach $A$-modules $X$ for which there exists a commutative unital $C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive unital homomorphism $θ\colon A\to C(K)$ such that $i(a\cdotp x) =θ(a)i(x)$ for ... View More