BANACH ALGEBRA BUNDLES

If E is a fibre bundle over a space X with fibre A, a Banach algebra, and group the group of isometric automorphisms of A then the set of sections of the fibre bundle can be endowed with the structure of a Banach algebra. If the fibre A is a so-called Q-uniform Banach algebra (e.g., a commutative Banach algebra) then the maximal ideal space of the Banach algebra of sections can be identified as a fibre bundle with base Xy fibre the set of maximal ideals of the Banach algebra A and group the group of self-homeomorphisms of the space of maximal ideals of A. Similar results are obtained for certain epimorphism structures associated with the algebras described. © 1969 by Pacific Journal of Mathematics.