Sectional representation of Banach modules and their multipliers (Q1864317)

Summary: Let \(X\) be a Banach module over the commutative Banach algebra \(A\) with maximal ideal space \(\Delta\). We show that there is a norm-decreasing representation of \(X\) as a space of bounded sections in a Banach bundle \(\pi :\mathcal{E}\rightarrow \Delta\), whose fibers are quotient modules of \(X\). There is also a representation of \(M(X)\), the space of multipliers \(T:A\to X\), as a space of sections in the same bundle, but this representation may not be continuous. These sectional representations subsume results of various authors over the past three decades.