Mixing of Cartesian squares of positive operators

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3 Scopus citations


Let T be a power bounded positive operator in L 1(X, Σ, m)of a probability space, given by a transition measure P (x, A). The Cartesian square S is the operator on L 1 (X × X, Σ × Σ, m × m) induced by the transition measure Q((x, y), A × B)=P(x, A)P(y, B). T is completely mixing if ∝u e dm=0 implies T n u→0 weakly (where 0≦e ∈L with T * e=e). Theorem. If T has no fixed points, then T is completely mixing if and only if S is completely mixing.

Original languageEnglish
Pages (from-to)349-354
Number of pages6
JournalIsrael Journal of Mathematics
Issue number4
StatePublished - 1 Dec 1972
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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