Vol. 39, No. 3, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 311: 1
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On the ratio ergodic theorem for semi-groups

Humphrey Sek-Ching Fong and Louis Sucheston

Vol. 39 (1971), No. 3, 659–667

For a semi-group Γ of positive linear contractions on L1 of a σ-finite measure space (X,𝒜), strongly continuous on (0,), there are two ratio ergodic theorems: one, due to Chacon and Ornstein, describes the behavior at infinity; the other one, due to Krengel-Ornstein-Akcoglu-Chacon, describes the “local” behavior. In the present paper we attempt to generalize these results to the case when the semigroup is only uniformly bounded. Then the space X decomposes into two parts, Y and Z, called the remaining and the disappearing part, and both ratio theorems are shown to hold on Y . The ratio theorem at infinity fails on Z.

Mathematical Subject Classification
Primary: 47D05
Secondary: 28A65
Received: 26 January 1970
Published: 1 December 1971
Humphrey Sek-Ching Fong
Louis Sucheston