| A Lower Bound for the Differences of Powers of Linear Operators |
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| 作者姓名： | J. MALINEN O. NEVANLINNA V. TURUNEN Z. YUAN |
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| 作者单位： | Department of Mathematics, Helsinki University of Technology, P. O. Box 1100 FIN-02015 HUT, Finland |
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| 摘 要： | 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： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.
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| 关 键 词： | 线性算子 幂差 下界 Esterle-Berkani猜想 |
| 收稿时间： | 25 June 2004 |
| 修稿时间： | 2004-05-252004-09-15 |
A Lower Bound for the Differences of Powers of Linear Operators |
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| J. MALINEN O. NEVANLINNA V. TURUNEN Z. YUAN.A Lower Bound for the Differences of Powers of Linear Operators[J].Acta Mathematica Sinica,2007,23(4):745-748. |
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| Authors: | J Malinen O Nevanlinna V Turunen Z Yuan |
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| Institution: | (1) Department of Mathematics, Helsinki University of Technology, 1100, FIN-02015 HUT, Finland |
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| 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. |
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| Keywords: | Esterle– Berkani’ s conjecture Quasi– nilpotent linear operator Differences of powers Decay |
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