A Multiple Sequence Ergodic Theorem

Abstract

Abstract Let be a σ-finite measure space, {T 1 , …, T k } a set of linear operators of , some p, 1≤p≤∞.If exists a.e. for all f ∊ L p , we say that the multiple sequence ergodic theorem holds for {T 1 , …, T k }. If f ≥0 implies Tf≥0, we say that T is positive. If there exists an operator S such that |Tf(x)|≥S |f|(x) a.e., we say that T is dominated by S . In this paper we prove that if T 1 , …, T k are dominated by positive contractions of , p fixed, 1<p<∞, then the multiple sequence ergodic theorem holds for {T 1 , …, T k }.

Locations

• Canadian Mathematical Bulletin - View - PDF