English

Less than one implies zero

Functional Analysis 2016-09-29 v2

Abstract

In this paper we show that from the estimate supt0C(t)cos(at)I<1\sup_{t \geq 0}\|C(t) - \cos(at)I\| <1 we can conclude that C(t)C(t) equals cos(at)I\cos(at) I. Here (C(t))t0\left(C(t)\right)_{t \geq 0} is a strongly continuous cosine family on a Banach space.

Cite

@article{arxiv.1310.6202,
  title  = {Less than one implies zero},
  author = {Felix Schwenninger and Hans Zwart},
  journal= {arXiv preprint arXiv:1310.6202},
  year   = {2016}
}

Comments

Corrected the previous version (in particular, a mistake in Lemma 2.1), streamlined and added recent references (see Introduction). 6 pages

R2 v1 2026-06-22T01:52:25.422Z