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A reduction theorem for the topological degree for mappings of class

Author(s): J. Berkovits
Journal: Proc. Amer. Math. Soc. 135 (2007), 2059-2064.
MSC (2000): Primary 47H11, 47J05
Posted: 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 from a real separable reflexive Banach space into the dual space can be reduced into the calculation of degree of mapping from a closed subspace $V\subset X$ into Since the Leray-Schauder mappings are acting from to and we are dealing with mappings from to the standard `invariant subspace' condition must be replaced by a less obvious one.

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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

DOI: 10.1090/S0002-9939-07-08748-5
PII: S 0002-9939(07)08748-5
Keywords: Topological degree, class $(S_+)$, reduction theorem
Received by editor(s): March 2, 2006
Posted: February 2, 2007
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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