Property($K^*$) Implies the Weak Fixed Point Property

TL;DR

This paper proves that if the dual of a separable Banach space has Property(K*), then the space itself has the weak fixed point property, advancing previous results in the field.

Contribution

It establishes a new link between Property(K*) of the dual space and the weak fixed point property of the original space, improving prior theorems.

Findings

Dual of a separable Banach space with Property(K*) has the weak fixed point property.

Improves upon previous results relating dual properties to fixed point properties.

Provides new conditions under which the weak fixed point property holds.

Abstract

It is shown that if the dual of a separable Banach space has Property($K^*$) then the original space has the weak fixed point property. This is an improvement of previously results.