Equivariant absolute extensor property on hyperspaces of convex sets

2014/01/12 by Natalia Jonard-Pérez, Jonard-Pérez, Natalia
Mathematics · #52A07 #52A20 #54B20 #54C55 #57N20 #57S10 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Metric Geometry (math.MG) #math.FA #math.GN #math.MG #msc:52A07 #msc:52A20 #msc:54B20 #msc:54C55 #msc:57N20 #msc:57S10

paper · pdf · doi:10.48550/arxiv.1401.2653

8 pages

arxiv created 2014/02/07 · arxiv updated 2014/02/10

Abstract

Let G be a compact group acting on a Banach space L by means of linear isometries. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact convex subsets of L endowed with the Hausdorff metric topology. The main result of this paper states that the G-space cc(L) is a G-AE. Under some extra assumptions, this result can be extended to CB(L), the hyperspace of all closed and bounded convex subsets of L.

Related

• Extension properties of orbit spaces of proper actions revisited
• Partial actions of groups on hyperspaces
• Extension properties of orbit spaces for proper actions revisited
• Equivariant geometry of Banach spaces and topological groups
• Invariant strictly convex renormings