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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 3, 2003, pp. 619–645
DOI: 10.4171/ZAA/1166

Published online: 2003-09-30

About the Sign of Oriented Fredholm Operators between Banach Spaces

Pierluigi Benevieri[1], Massimo Furi[2], Maria Patrizia Pera[3] and Marco Spadini[4]

(1) Universita di Firenze, Italy
(2) Università di Firenze, Italy
(3) Universita di Firenze, Italy
(4) Universita di Firenze, Italy

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.

Keywords: Linear Fredholm operators, orientation, sign jump, Banach spaces

Benevieri Pierluigi, Furi Massimo, Pera Maria Patrizia, Spadini Marco: About the Sign of Oriented Fredholm Operators between Banach Spaces. Z. Anal. Anwend. 22 (2003), 619-645. doi: 10.4171/ZAA/1166