Uniform ergodic theorems for locally integrable semigroups and pseudoresolvents

Shaw, Sen-Yen

doi:10.1090/S0002-9939-1986-0848876-0

Uniform ergodic theorems for locally integrable semigroups and pseudoresolvents
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Proc. Amer. Math. Soc. 98 (1986), 61-67 Request permission

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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Functional analysis