Coincidence index and multiplicity

This paper is devoted to the extension, in the frame of coincidence degree theory in normed spaces, of the concept of Leray-Schauder index of an isolated fixed point. The generalization includes basic properties of the coincidence index, Krasnosel'skiĭ type theorems for the case of noninvertible linear part and a Leray-Schauder's type formula relating the index and spectral theory in the linear case. This last problem needs the introduction of the concept of characteristic value for some couples of linear mappings and of its multiplicity.