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arXiv · 2405.15910

On asymptotic B-convexity and infratype

Florent Baudier·Audrey Fovelle
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Abstract

In this note, we introduce and study the notions of asymptotic B-convexity and asymptotic infratype $p$, and we prove asymptotic analogs of a series of results due to Giesy \cite{Giesy66} and Pisier \cite{Pisier74}. In particular, we give a simplified proof of an asymptotic version of Pisier's $\ell_1$-theorem that was originally proven by Causey, Draga, and Kochanek in \cite{CDK19}. We also briefly discuss the notion of asymptotic stable type.

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Florent Baudier, Audrey Fovelle. 2024-05-24. On asymptotic B-convexity and infratype. https://arxiv.org/abs/2405.15910

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