A reduction theorem for the topological degree for mappings of class $(S+)$
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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.References
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Additional Information
- J. Berkovits
- Affiliation: Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland
- Email: juha.berkovits@oulu.fi
- Received by editor(s): March 2, 2006
- Published electronically: February 2, 2007
- Communicated by: Jonathan M. Borwein
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2059-2064
- MSC (2000): Primary 47H11, 47J05
- DOI: https://doi.org/10.1090/S0002-9939-07-08748-5
- MathSciNet review: 2299481