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A new convexity property that implies a fixed point property for $L_{1}$

Chris Lennard — 1991

Studia Mathematica

In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result...

Characterization of L...(R...) Using Gabor Frames.

Loukas Grafakos; Chris Lennard — 2001

The journal of Fourier analysis and applications [[Elektronische Ressource]]

A contractive fixed point free mapping on a weakly compact convex set

Jared Burns; Chris Lennard; Jeromy Sivek — 2014

Studia Mathematica

We prove the existence of a contractive mapping on a weakly compact convex set in a Banach space that is fixed point free. This answers a long-standing open question.

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A new convexity property that implies a fixed point property for L 1

Characterization of L...(R...) Using Gabor Frames.

A contractive fixed point free mapping on a weakly compact convex set

A new convexity property that implies a fixed point property for $L_{1}$