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Existence of Invariant Weak Units in Banach Lattices: Countably Generated Left Amenable Semigroup of Operators

Published online by Cambridge University Press:  20 November 2018

K. Prabaharan
Affiliation:
Department of Mathematics Ohio State University Columbus, Ohio 43210, U.S.A.
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Abstract

Let Σ be a countably generated left amenable semigroup and ﹛Tσ| σ ∈ Σ﹜ be a representation of Σ as a semigroup of positive linear operators on a weakly sequentially complete Banach lattice E with a weak unit e. It is assumed are uniformly bounded. It is shown that a necessary and sufficient condition for the existence of a weak unit invariant under ﹛Tσ | σ ∈ Σ﹜ is that inf σ∈Σ H(Tσe) > 0 for all nonzero H in the positive dual cone of E.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

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