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

Prabaharan, K.

Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1299-1312

Résumé

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 Tσ 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.

Détail

DOI : 10.4153/CJM-1993-073-1

Mots-clés : 46B30, 47B55, 28D15

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