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Transactions of the American Mathematical Society Series B

ISSN 2330-0000



Fixed points in convex cones

Author: Nicolas Monod
Journal: Trans. Amer. Math. Soc. Ser. B 4 (2017), 68-93
MSC (2010): Primary 47H10
Published electronically: July 19, 2017
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Abstract: We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous representations, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem for Banach spaces. When restricting to cones that are locally compact in the weak topology, we prove that the property holds for all distal actions, thus extending the general Ryll-Nardzewski theorem for all locally convex spaces.

Returning to arbitrary actions, the proposed fixed-point property becomes a group property, considerably stronger than amenability. Equivalent formulations are established and a number of closure properties are proved for the class of groups with the fixed-point property for cones.

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Additional Information

Nicolas Monod
Affiliation: EPFL, 1015 Lausanne, Switzerland

Received by editor(s): January 23, 2017
Received by editor(s) in revised form: February 10, 2017
Published electronically: July 19, 2017
Article copyright: © Copyright 2017 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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