Über das wachstum von resolventen in der nähe einer isolierten singularität

Let L(λ) be a bundle of linear bounded operators between two Banach spaces. In this paper we study the behaviour of {L(λ)}^?1, if λ tends to λ_o and L(λ_o) is a Fredholm operator with index 0. We show that the growth of this resolvent can be described by the length of certain chains of generalized principal vectors; if L(λ) depends analytically on the parameter λ, we get a complete characterization for an isolated singularity of L, and also a Laurent expansion for the resolvent. Finally, we give applications to a broad class of bundles of bounded self-adjoint operators.