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 X, 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.
