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- W4286987488 abstract "Given a bounded convex subset $C$ of a Banach space $X$ and a free ultrafilter $mathcal U$, we study which points $(x_i)_mathcal U$ are extreme points of the ultrapower $C_mathcal U$ in $X_mathcal U$. In general, we obtain that when ${x_i}$ is made of extreme points (respectively denting points, strongly exposed points) and they satisfy some kind of uniformity, then $(x_i)_mathcal U$ is an extreme point (respectively denting point, strongly exposed point) of $C_mathcal U$. We also show that every extreme point of $C_{mathcal U}$ is strongly extreme, and that every point exposed by a functional in $(X^*)_{mathcal U}$ is strongly exposed, provided that $mathcal U$ is a countably incomplete ultrafilter. Finally, we analyse the extremal structure of $C_mathcal U$ in the case that $C$ is a super weakly compact or uniformly convex set." @default.
- W4286987488 created "2022-07-25" @default.
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- W4286987488 date "2021-09-03" @default.
- W4286987488 modified "2023-09-26" @default.
- W4286987488 title "Extremal structure in ultrapowers of Banach spaces" @default.
- W4286987488 doi "https://doi.org/10.48550/arxiv.2109.01393" @default.
- W4286987488 hasPublicationYear "2021" @default.
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