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An Abel-maximal ergodic
theorem for semi-groups
Ryōtarō Satō |
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Vol. 51 (1974), No. 2, 543–547
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Abstract |
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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
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Milestones
Received: 4 January 1973
Published: 1 April 1974
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Authors |
| Ryōtarō Satō | |
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