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

Author: J. Berkovits
Journal: Proc. Amer. Math. Soc. 135 (2007), 2059-2064
MSC (2000): Primary 47H11, 47J05
Published electronically: February 2, 2007
MathSciNet review: 2299481
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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 $ V\subset 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.

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J. Berkovits
Affiliation: Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland

Keywords: Topological degree, class $(S_+)$, reduction theorem
Received by editor(s): March 2, 2006
Published electronically: February 2, 2007
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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