Zeitschrift für Analysis und ihre Anwendungen 22 (2003), No. 3, 619--645
Copyright Heldermann Verlag 2003
About the Sign of Oriented Fredholm Operators between Banach Spaces
Pierluigi Benevieri
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy
Massimo Furi
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy
Maria Patrizia Pera
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta 3, 50139 Firenze, Italy
Marco Spadini
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta 3, 50139 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.
MSC: 47A53; 47E05, 34B05
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