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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 V C 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.

A reduction theorem for the topological degree for mappings of class (𝑆+)