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
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.
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.