We give conditions for an oriented family of bounded Fredholm operators of index zero between Banach spaces to have a sign jump. In particular, we discuss criteria for detecting the sign jump in some special situations. For instance, when a sort of Crandall-Rabinowitz condition for bifurcation is assumed or in the case of a family of Leray-Schauder type. Finally, some examples of ordinary differential operators are presented to illustrate the meaning of the abstract results.
Cite this article
Pierluigi Benevieri, Massimo Furi, Maria Patrizia Pera, Marco Spadini, About the Sign of Oriented Fredholm Operators between Banach Spaces. Z. Anal. Anwend. 22 (2003), no. 3, pp. 619–645DOI 10.4171/ZAA/1166