Support overlapping $L_{1}$ contractions and exact non-singular transformations
Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 515-520
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Let T be a positive linear contraction of $L_{1}$ of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.
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Michael Lin. Support overlapping $L_{1}$ contractions and exact non-singular transformations. Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 515-520. doi: 10.4064/cm-84/85-2-515-520
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