A lower bound for the differences of powers of linear operators

Research output: Contribution to journalArticleScientificpeer-review

Standard

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

In: ACTA MATHEMATICA SINICA : ENGLISH SERIES, Vol. 23, No. 4, 2007, p. 745-748.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

Bibtex - Download

@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",

}

RIS - Download

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