Bundles of Banach algebras (Q1338418)

Summary: We study bundles of Banach algebras \(\pi: A\to X\), where each fiber \(A_ X= \pi^{-1}(\{x\})\) is a Banach algebra and \(X\) is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra \(\Gamma(\pi)\) relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle \(\pi: A\to X\) relates to the standard adjunction of identities to the fibers.