Less than one implies zero

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    Abstract

    In this paper we show that from an estimate of the form supt≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.

    Original languageEnglish
    Pages (from-to)181-188
    Number of pages8
    JournalStudia mathematica
    Volume229
    Issue number2
    DOIs
    Publication statusPublished - 2015

    Keywords

    • Cosine families
    • Operator cosine functions
    • Zero-one-law

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