On dominant contractions and a generalization of the zero–two law
Zaharopol proved the following result: let T, S : L1(X,F,μ) → L1(X,F,μ) be two positive contractions such that T ≤ S. If ||S−T|| < 1 then ||Sn − T n||<1 for all n ∈ N. In the present paper we generalize this result to multi-parameter contractions acting on L1. As an application of that result...
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| Format: | Article |
| Language: | English |
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Birkhäuser Basel
2011
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| Online Access: | http://irep.iium.edu.my/6518/ http://irep.iium.edu.my/6518/ http://irep.iium.edu.my/6518/ http://irep.iium.edu.my/6518/1/mf-positivity%282011%29.pdf |
| Summary: | Zaharopol proved the following result: let T, S : L1(X,F,μ) → L1(X,F,μ) be two positive contractions such that T ≤ S. If ||S−T|| < 1 then ||Sn − T n||<1 for all n ∈ N. In the present paper we generalize this result to multi-parameter contractions acting on L1. As an application of that result we prove a generalization of
the “zero–two” law. |
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