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A reduction theorem for the topological degree for mappings of class
Authors:J. Berkovits
Affiliation:Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland
Abstract:
The reduction theorem for the Leray-Schauder degree provides an efficient tool to calculate the value of the degree in a suitable invariant subspace. We shall prove how the calculation of the value of the topological degree for a mapping of class $ (S_+)$ from a real separable reflexive Banach space $ X$ into the dual space $ X^*$ can be reduced into the calculation of degree of mapping from a closed subspace $ Vsubset X$ into $ V^*.$ Since the Leray-Schauder mappings are acting from $ X$ to $ X$ and we are dealing with mappings from $ X$ to $ X^*,$ the standard `invariant subspace' condition must be replaced by a less obvious one.

Keywords:Topological degree   class $(S_+)$   reduction theorem
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