A generalized frame bundle for certain Fréchet vector bundles and linear connections
The authors consider a projective system of Banach vector bundles whose limit is a Fréchet bundle \(E\) of type fibre \(F\) and construct a generalized bundle of frames \(P(E)\) of \(E\) by revising entirely the classical notion and by substituting \(GL(F)\) with an appropriate enlarged structure group. It is proved that \(E\) is associated with \(P(E)\) and linear connections of \(E\) correspond to principal connections of \(P(E)\). For related work, see \textit{E. Vassiliou} [Period. Math. Hung. 13, 289-308 (1982; Zbl 0525.53044)] and \textit{T. Sakurai} and \textit{T. Nono} [Bull. Fukuoka Univ. Educ., Part III 30, 17-27 (1980; Zbl 0469.58001)].
scientific article; zbMATH DE number 1054596