The Cayley transform of the generator of a bounded C0-semigroup

A. Gomilko, Heiko J. Zwart

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)

    Abstract

    Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$
    Original languageUndefined
    Article number10.1007/s00233-006-0648-8
    Pages (from-to)140-148
    Number of pages9
    JournalSemigroup forum
    Volume74
    Issue number1/1
    DOIs
    Publication statusPublished - Feb 2007

    Keywords

    • MSC-93C25
    • IR-63698
    • EWI-8191
    • METIS-241701

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