International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 13, Pages 817-825
doi:10.1155/S0161171203207109

Sectional representation of Banach modules and their multipliers

Abstract

Let X be a Banach module over the commutative Banach algebra A with maximal ideal space Δ. We show that there is a norm-decreasing representation of X as a space of bounded sections in a Banach bundle π:ℰ→Δ, whose fibers are quotient modules of X. There is also a representation of M(X), the space of multipliers T:A→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.