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arXiv · 1505.06065

A short proof of the zero-two law for cosine functions

Jean Esterle
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Abstract

Let $(C(t))\in\mathbb{R}}$ be a cosine function in a unital Banach algebra. We give a simple proof of the fact that if lim sup$\_{t\to 0}\vert C(t)-1\_A\vert\textless{}2,$ then $lim sup\_{t\to 0}\Vert C(t)-1\_A\Vert=0.$

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Jean Esterle. 2015-05-22. A short proof of the zero-two law for cosine functions. https://arxiv.org/abs/1505.06065

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