English

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

Functional Analysis 2015-05-25 v1

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_t0C(t)1_A\textless2,\_{t\to 0}\vert C(t)-1\_A\vert\textless{}2, then limsup_t0C(t)1_A=0.lim sup\_{t\to 0}\Vert C(t)-1\_A\Vert=0.

Keywords

Cite

@article{arxiv.1505.06065,
  title  = {A short proof of the zero-two law for cosine functions},
  author = {Jean Esterle},
  journal= {arXiv preprint arXiv:1505.06065},
  year   = {2015}
}