## Abstract

Let T be a bounded linear operator in a Banach space, with σ(T) = {1}. In 1983, Esterle–Berkani’ s conjecture was proposed for the decay of differences (I − T) T n as follows: Either

lim inf n →∞ (n + 1)∥ (I − T) T n ∥ ≥ 1/e

or T = I. We prove this claim and discuss some of its consequences.

lim inf n →∞ (n + 1)∥ (I − T) T n ∥ ≥ 1/e

or T = I. We prove this claim and discuss some of its consequences.

Original language | English |
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Pages (from-to) | 745-748 |

Journal | ACTA MATHEMATICA SINICA : ENGLISH SERIES |

Volume | 23 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- Esterle–Berkani’s conjecture
- Quasi–nilpotent linear operator
- Differences of powers
- Decay