Banach空间中序列的子平均

IF 0.1 Q4 MATHEMATICS Real Analysis Exchange Pub Date : 2023-10-01 DOI:10.14321/realanalexch.48.2.1665637941

Morgan O'Brien

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摘要

对于Banach空间$\mathcal{X}$中的序列，已知序列的子序列极限集合形成$\mathcal{X}$的闭子集。类似地，如果序列是收敛的，那么它的Cesàro平均值序列也收敛到相同的值。在本文中，我们利用遍历理论研究了Banach空间中给定序列的子序列的Cesàro极限集的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Subsequential Averages of Sequences in Banach Spaces

For a sequence in a Banach space $\mathcal{X}$, it is known that the set of subsequential limits of the sequence forms a closed subset of $\mathcal{X}$. Similarly, if the sequence is convergent, then the sequence of its Cesàro averages also converge to the same value. In this article, we study the properties of the set of Cesàro limits of subsequences of a given sequence in a Banach space using techniques from ergodic theory.

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