SECTIONAL REPRESENTATIONS OF BANACH MODULES

This paper is concerned with the representation of Banach algebras and Banach modules as sections of bundles of Banach spaces. In particu-lar. (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. The present paper extends and generalizes earlier results to be found in [7] and [8], to which the reader is referred for terminology and notations. Both of these papers center upon the study of sectional repre-sentations of "Gelfand type " for Banach modules (M, A) such that (1) the algebra ^ is commutative, an