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arXiv · 2411.17380

Fekete's lemma in Banach spaces

Aleksei Kulikov·Feng Shao
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Abstract

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.

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BibTeXRIS

Aleksei Kulikov, Feng Shao. 2024-11-26. Fekete's lemma in Banach spaces. https://arxiv.org/abs/2411.17380

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