Vol. 51, No. 2, 1974

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An Abel-maximal ergodic theorem for semi-groups

Ryōtarō Satō

Vol. 51 (1974), No. 2, 543–547
Abstract

The purpose of this paper is to prove a maximal ergodic theorem for Abel means of a strongly measurable semi-group Γ = {Tt;t 0} of linear contractions on a complex L1-space satisfying |Ttf|c a.e. for any t 0 and any integrable f with |f|c a.e. Applying the obtained maximal ergodic theorem, individual and dominated ergodic theorems for Abel means are also proved. These results extend results obtained by D. A. Edwards for sub-Markovian semi-groups.

Mathematical Subject Classification 2000
Primary: 47A35
Secondary: 28A65
Milestones
Received: 4 January 1973
Published: 1 April 1974
Authors
Ryōtarō Satō