Abstract
Necessary and sufficient conditions are presented for the Abel averages of discrete and strongly continuous semigroups, T k and T t , to be power convergent in the operator norm in a complex Banach space. These results cover also the case where T is unbounded and the corresponding Abel average is defined by means of the resolvent of T. They complement the classical results by Michael Lin establishing sufficient conditions for the corresponding convergence for a bounded T.
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Acknowledgments
This work was supported by the DFG through SFB 701 and the project 436 POL 113/125/0-1 and also by the European Commission project TODEQ (MTKD-CT-2005-030042). The authors are grateful to the referee for suggestions to Section 3.
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Kozitsky, Y., Shoikhet, D. & Zemánek, J. Power convergence of Abel averages. Arch. Math. 100, 539–549 (2013). https://doi.org/10.1007/s00013-013-0515-2
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DOI: https://doi.org/10.1007/s00013-013-0515-2