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A Mean Ergodic Theorem for Multiparameter Superadditive Processes on Banach Lattices

Published online by Cambridge University Press:  20 November 2018

Felix Lee
Felix Lee*
Affiliation:
Redeemer College, Ancaster, Ont L96 3N6
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Let E be a Banach Lattice. We will consider E to be weakly sequentially complete and to have a weak unit u. Thus we may represent E as a lattice of real valued functions defined on a measure space (χ, , μ). There is a set R ⊂ χ such that R supports a maximal invariant function Φ for a postive contraction T on E [5]. Let N = χ — R be the complement of R. Akcoglu and Sucheston showed that where E+ is the positive cone of E. If in addition a monotone condition (UMB) is satisfied, then the same authors showed [4] that converges in norm.

Keywords

47B5547A3528D05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 1018 - 1040
Copyright
Copyright © Canadian Mathematical Society 1990

References

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