Power‐Bounded Operators and Related Norm Estimates
By Nigel J. Kalton, Stephen Montgomery-Smith, Krzysztof Oleszkiewicz, Yuri Tomilov. 2002
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It is considered whether L=limsupn→∞n‖Tn+1−Tn‖<∞ implies that the operator T is power‐bounded. It is shown that this is so if L<1/e, but it does not necessarily hold if L=1/e. As part of the methods, a result of Esterle is improved, showing that if σ(T)={1} and T{≠}I, then liminfn→∞n‖Tn+1−Tn‖⩾1/e. The constant 1/e is sharp. Finally, a way to create many generalizations of Esterle's result is described, and also many conditions are given on an operator which imply that its norm is equal to its spectral radius.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/7ebfb5a6ddfa5421e062e6c7d4c38e065bf24be2
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In Applied Mathematics
Citations in the corpus
- Uniform Abel–Kreiss Boundedness and the Extremal Behaviour of the Volterra Operator (2005, background): “The extremal situation n 1 may also happen but with larger spectrum; see [10].”