On asymptotic B-convexity and infratype
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913362496978944 |
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| author | Baudier, Florent Fovelle, Audrey |
| author_facet | Baudier, Florent Fovelle, Audrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On asymptotic B-convexity and infratype Baudier, Florent Fovelle, Audrey Functional Analysis 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. |
| title | On asymptotic B-convexity and infratype |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.15910 |