### Abstract

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 language | English |
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Pages (from-to) | 1721-1741 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 363 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 |

### Keywords

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

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## Cite this

Dungey, N. (2011). Subordinated discrete semigroups of operators.

*Transactions of the American Mathematical Society*,*363*(4), 1721-1741. https://doi.org/10.1090/S0002-9947-2010-05094-9