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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Uniform ergodic theorems for locally integrable semigroups and pseudoresolvents

Author: Sen-Yen Shaw
Journal: Proc. Amer. Math. Soc. 98 (1986), 61-67
MSC: Primary 47A35; Secondary 47D05
MathSciNet review: 848876
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Abstract: We study uniform ergodicity (at $ \infty $) of a locally integrable operator semigroup $ T( \cdot )$ of type $ {w_0}$ under a suitable condition which is weaker than the usual one $ {w_0} \leqslant 0$. We also give a precise characterization of the uniform Cesàro-ergodicity for semigroups of class $ (0,A)$. To prove the part of Abel-ergodicity we first prove a general uniform ergodic theorem for pseudo-resolvents.

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Keywords: Cesàro-ergodicity, Abel-ergodicity, locally integrable semigroup, Laplace transform, pseudo-resolvent
Article copyright: © Copyright 1986 American Mathematical Society

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