# Support overlapping ${L}_{1}$ contractions and exact non-singular transformations

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 515-520
- ISSN: 0010-1354

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topLin, Michael. "Support overlapping $L_{1}$ contractions and exact non-singular transformations." Colloquium Mathematicae 84/85.2 (2000): 515-520. <http://eudml.org/doc/210830>.

@article{Lin2000,

abstract = {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.},

author = {Lin, Michael},

journal = {Colloquium Mathematicae},

keywords = {completely mixing; asymptotic stability; overlapping supports; Perron-Frobenius operator; Harris recurrent contraction},

language = {eng},

number = {2},

pages = {515-520},

title = {Support overlapping $L_\{1\}$ contractions and exact non-singular transformations},

url = {http://eudml.org/doc/210830},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Lin, Michael

TI - Support overlapping $L_{1}$ contractions and exact non-singular transformations

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 515

EP - 520

AB - 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.

LA - eng

KW - completely mixing; asymptotic stability; overlapping supports; Perron-Frobenius operator; Harris recurrent contraction

UR - http://eudml.org/doc/210830

ER -

## References

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