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THE LERAY-SCHAUDER ALTERNATIVE FOR NONEXPANSIVE MAPS FROM THE BALL CHARACTERIZE HILBERT SPACE

Ireland, Michael and Kirk, William A. and Sims, Brailey (1999) THE LERAY-SCHAUDER ALTERNATIVE FOR NONEXPANSIVE MAPS FROM THE BALL CHARACTERIZE HILBERT SPACE. In: Nonlinear Analysis and Convex Analysis: Proceedings of the International Conference Niigata, Japan 28-31 July 1998. Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis . World Sci. Publishing, River Edge, NJ, pp. 167-172. ISBN 9789810240745

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    Abstract

    We show that for a nonexpansive map from the unit ball of a Hilbert space into the space the existence of a fixed point and the Leray-Schauder alternative are mutually exclusive alternatives, and that this characterizes Hilbert space. The equivalence of several formulations of the Leray-Schauder alternative is also established.

    Item Type: Book Section
    Uncontrolled Keywords: Hilbert space, nonexpansive mapping, fixed point, Leray-Schauder alternative principle, extension property.
    Subjects: 47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    Faculty: UNSPECIFIED
    Depositing User: Mr Christopher Maitland
    Date Deposited: 07 Apr 2011 10:42
    Last Modified: 07 Apr 2011 10:42
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/865

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