Fekete's lemma in Banach spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916496599416832 |
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| author | Kulikov, Aleksei Shao, Feng |
| author_facet | Kulikov, Aleksei Shao, Feng |
| contents | For a sequence of vectors $\{v_n\}_{n\in\mathbb{N}}$ in the uniformly convex Banach space $X$ which for all $n, m\in \mathbb{N}$ satisfy $\|v_{n+m}\|\le \|v_n + v_m\|$ we show the existence of the limit $\lim_{n\to \infty} \frac{v_n}{n}$. This extends the classical Fekete's subadditivite lemma to Banach space-valued sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fekete's lemma in Banach spaces Kulikov, Aleksei Shao, Feng Functional Analysis Metric Geometry For a sequence of vectors $\{v_n\}_{n\in\mathbb{N}}$ in the uniformly convex Banach space $X$ which for all $n, m\in \mathbb{N}$ satisfy $\|v_{n+m}\|\le \|v_n + v_m\|$ we show the existence of the limit $\lim_{n\to \infty} \frac{v_n}{n}$. This extends the classical Fekete's subadditivite lemma to Banach space-valued sequences. |
| title | Fekete's lemma in Banach spaces |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2411.17380 |