Banach bundle

Summary

A Banach bundle is a vector bundle whose fibres are Banach spaces, possibly infinite-dimensional, over a Banach manifold. The transition maps between local trivialisations must vary smoothly in the operator norm. Tangent bundles of Banach manifolds are Banach bundles, and so are the bundles of Sobolev sections that appear in nonlinear analysis on manifolds. Many constructions of moduli spaces present the moduli space as the zero set of a section of a Banach bundle.