About the sign of oriented Fredholm operators between Banach spaces (Q1431146)

In [\textit{P. Benevieri} and \textit{M. Furi}, Ann. Sci. Math. Qué. 22, No. 2, 131--148 (1998; Zbl 1058.58502)] there was introduced a notion of orientation for linear Fredholm operators of index zero between real vector spaces. This notion permits to determine the sign of a bounded Fredholm operator of index zero between real Banach spaces. In the paper under review, there are given conditions for an oriented family of the last mentioned operators to have a sign jump. In particular, there are discussed criteria for detecting the sign jump in some special situations. Some examples of ordinary differential operators are presented as illustration.