Subordinated discrete semigroups of operators

Nick Dungey

    Research output: Contribution to journalArticlepeer-review

    21 Citations (Scopus)


    Given a power-bounded linear operator T in a Banach space and a probability F on the non-negative integers, one can form a 'subordinated' operator S = ∑k≥0 F(k)Tk. We obtain asymptotic properties of the subordinated discrete semigroup (Sn : n = 1, 2, ⋯) under certain conditions on F. In particular, we study probabilities F with the property that S satisfies the Ritt resolvent condition whenever T is power-bounded. Examples and counterexamples of this property are discussed. The hypothesis of power-boundedness of T can sometimes be replaced by the weaker Kreiss resolvent condition.
    Original languageEnglish
    Pages (from-to)1721-1741
    Number of pages21
    JournalTransactions of the American Mathematical Society
    Issue number4
    Publication statusPublished - 2011


    • Analytic semigroup
    • Discrete semigroup
    • Power-bounded operator
    • Ritt operator
    • Subordinated semigroup


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