It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux ([C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793]), arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.

中文翻译：

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沿李群和 BANACH 代数中的规定序列逃离邻域

结果表明，Jamison 序列，由 Badea 和 Grivaux 于 2007 年引入（[C. Badea 和 S. Grivaux，单模特征值，均匀分布序列和线性动力学，Adv. Math. 211 (2007), no. 2, 766-- 793])，自然地出现在研究没有小子群的拓扑群、Banach 或规范代数元素中，它们的权力接近于沿子序列的恒等式，以及（自伴随）正算子的特征化，通过它们的一些增加权力。这些结果的共同核心是对那些序列的描述，对于这些序列，李群或赋范代数中的非同一元素在属于给定序列的多个步骤中逃脱了同一的任意小邻域。给出了贾米森序列的几个光谱特征，并证明了其他相关结果。