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 -