Convexification of super weakly compact sets and measure of super weak noncompactness

Tu, Kun

doi:10.1090/proc/15393

Convexification of super weakly compact sets and measure of super weak noncompactness
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Proc. Amer. Math. Soc. 149 (2021), 2531-2538 Request permission

Abstract:

In the paper, we give a quantitative version of the positive answer to the open question about the convex hull of a super weakly compact set. Measure of super weak noncompactness $\sigma$ is introduced and proved to share several nice properties with the Hausdorff measure of noncompactness. As an application, a fixed point theorem for $\sigma$-condensing maps is given.

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