Vol. 28, No. 2, 1969

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Banach algebra bundles

Bernard Russel Gelbaum

Vol. 28 (1969), No. 2, 337–349

If 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.

Mathematical Subject Classification
Primary: 46.50
Received: 19 January 1968
Published: 1 February 1969
Bernard Russel Gelbaum