# A lower bound for the differences of powers of linear operators

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**A lower bound for the differences of powers of linear operators.** / Malinen, Jarmo; Nevanlinna, Olavi; Turunen, Ville; Yuan, Zhijian.

Research output: Contribution to journal › Article › Scientific › peer-review

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*ACTA MATHEMATICA SINICA : ENGLISH SERIES*, vol. 23, no. 4, pp. 745-748. https://doi.org/10.1007/s10114-005-0765-4

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*ACTA MATHEMATICA SINICA : ENGLISH SERIES*,

*23*(4), 745-748. https://doi.org/10.1007/s10114-005-0765-4

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TY - JOUR

T1 - A lower bound for the differences of powers of linear operators

AU - Malinen, Jarmo

AU - Nevanlinna, Olavi

AU - Turunen, Ville

AU - Yuan, Zhijian

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Esterle–Berkani’s conjecture

KW - Quasi–nilpotent linear operator

KW - Differences of powers

KW - Decay

U2 - 10.1007/s10114-005-0765-4

DO - 10.1007/s10114-005-0765-4

M3 - Article

VL - 23

SP - 745

EP - 748

JO - ACTA MATHEMATICA SINICA : ENGLISH SERIES

T2 - ACTA MATHEMATICA SINICA : ENGLISH SERIES

JF - ACTA MATHEMATICA SINICA : ENGLISH SERIES

SN - 1439-8516

IS - 4

ER -

ID: 16528745