Abstract
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 {double pipe}S-T{double pipe} < 1 then {double pipe}Sn-Tn{double pipe} < 1 for all n {e open} 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.
Original language | English |
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Pages (from-to) | 497-508 |
Number of pages | 12 |
Journal | Positivity |
Volume | 15 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2011 |
Externally published | Yes |
Keywords
- "Zero-two" law
- Dominant contraction
- Positive operator
ASJC Scopus subject areas
- Analysis
- Theoretical Computer Science
- General Mathematics