International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 13, Pages 817-825

Sectional representation of Banach modules and their multipliers

Terje Hõim and D. A. Robbins

Department of Mathematics, Trinity College, Hartford 06106-3100, CT, USA

Received 9 July 2002

Copyright © 2003 Terje Hõim and D. A. Robbins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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:Δ, whose fibers are quotient modules of X. There is also a representation of M(X), the space of multipliers T:AX, 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.