@article{1419816e97f140e5aa94ee22361e40cb,
title = "A lower bound for the differences of powers of linear operators",
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: Eitherlim inf n →∞ (n + 1)∥ (I − T) T n ∥ ≥ 1/eor T = I. We prove this claim and discuss some of its consequences.",
keywords = "Esterle–Berkani’s conjecture , Quasi–nilpotent linear operator, Differences of powers , Decay",
author = "Jarmo Malinen and Olavi Nevanlinna and Ville Turunen and Zhijian Yuan",
year = "2007",
doi = "10.1007/s10114-005-0765-4",
language = "English",
volume = "23",
pages = "745--748",
journal = "ACTA MATHEMATICA SINICA : ENGLISH SERIES",
issn = "1439-8516",
number = "4",
}