This paper is concerned with
the representation of Banach algebras and Banach modules as sections of bundles of
Banach spaces. In particular: (1) if A is a commutative Banach algebra, then A
may be represented by sections of a locally trivial canonical line bundle;
(2) if A is a Banach algebra which is represented as sections of a canonical
bundle of Banach algebras, then there is a natural way in which any Banach
module M over A can be represented by sections of a canonical bundle of
Banach modules over the corresponding algebra bundle. We also investigate
projective tensor products of bundles of Banach algebras and bundles of Banach
modules.
