Mixing for positive operators in Banach lattices

In this paper we extend M. Lin’s definition of mixing for positive contractions in L1(X,Σ,m) with m(X) = 1 to positive operators in Banach lattices with weak-order units, and we generalize Lin’s Theorem 2.1 (Z. Wahrsch. Verw. Gebiete 19 (1971) 231–249) to the case of power-bounded positive operators in KB-spaces. In the particular case of weakly compact power-bounded positive operators, the same theorem is extended to Banach lattices with order-continuous norms.  2003 Elsevier Science (USA). All rights reserved.