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Less than one implies zero

Volume 229 / 2015

Felix L. Schwenninger, Hans Zwart Studia Mathematica 229 (2015), 181-188 MSC: Primary 47D09; Secondary 47D06. DOI: 10.4064/sm8218-12-2015 Published online: 16 December 2015

Abstract

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

Authors

  • Felix L. SchwenningerDepartment of Applied Mathematics
    University of Twente
    P.O. Box 217
    7500 AE Enschede, The Netherlands
    and
    School of Mathematics and Natural Sciences
    Arbeitsgruppe Funktionalanalysis
    University of Wuppertal
    D-42119 Wuppertal, Germany
    e-mail
  • Hans ZwartDepartment of Applied Mathematics
    University of Twente
    P.O. Box 217
    7500 AE Enschede, The Netherlands
    e-mail

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