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/6518/1/mf-positivity%282011%29.pdf |
| _version_ | 1848776679840808960 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T14:33:56Z |
| format | Article |
| id | iium-6518 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:33:56Z |
| publishDate | 2011 |
| publisher | Birkhäuser Basel |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-65182011-11-21T18:21:03Z http://irep.iium.edu.my/6518/ On dominant contractions and a generalization of the zero–two law Mukhamedov, Farrukh QA Mathematics 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. Birkhäuser Basel 2011-09 Article PeerReviewed application/pdf en http://irep.iium.edu.my/6518/1/mf-positivity%282011%29.pdf Mukhamedov, Farrukh (2011) On dominant contractions and a generalization of the zero–two law. Positivity, 15 (3). pp. 497-508. ISSN 1385-1292 (P), 1572-9281 (O) http://www.springerlink.com/content/x1q75jh18420l20u/ 10.1007/s11117-010-0102-8 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh On dominant contractions and a generalization of the zero–two law |
| title | On dominant contractions and a generalization of the zero–two law |
| title_full | On dominant contractions and a generalization of the zero–two law |
| title_fullStr | On dominant contractions and a generalization of the zero–two law |
| title_full_unstemmed | On dominant contractions and a generalization of the zero–two law |
| title_short | On dominant contractions and a generalization of the zero–two law |
| title_sort | on dominant contractions and a generalization of the zero–two law |
| topic | QA Mathematics |
| url | 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 |