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ArticleOriginal scientific text

Title

Support overlapping L1 contractions and exact non-singular transformations

Authors 1

Affiliations

  1. Ben-Gurion University of the Negev, Beer-Sheva, Israel

Abstract

Let T be a positive linear contraction of L1 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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Colloquium Mathematicum
2000/84/85/2
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Pages:
515-520
Main language of publication
English
Received
1999-09-22
Published
2000
Exact and natural sciences