Israel Journal of Mathematics

, Volume 42, Issue 4, pp 300–308 | Cite as

On local ergodic convergence of semi-groups and additive processes

  • Michael Lin


We prove the local ergodic theorem inL : Let {T t}t>0 be a strongly continuous semi-group of positive operators onL 1. IfT t is continuous at 0, then ɛ−1 0 F T 1 * f(x)dtT 0 * f(x) a.e., for everyf∈L . The technique shows how to obtain theL p local ergodic theorems from theL 1-contraction case. It applies also to differentiation ofL p additive processes. Then-dimensional case, which is new, is proved by reduction to then-dimensionalL 1-contraction case, solved by M. Akcoglu and A. del Junco.


Positive Operator Additive Process Order Interval Positive Linear Operator Strong Continuity 
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Copyright information

© The Weizmann Science Press of Israel 1982

Authors and Affiliations

  • Michael Lin
    • 1
  1. 1.Department of MathematicsBen Gurion University of the NegevBeer ShebaIsrael

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