On dominant contractions and a generalization of the zero-two law

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5 Citations (Scopus)

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 languageEnglish
Pages (from-to)497-508
Number of pages12
JournalPositivity
Volume15
Issue number3
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

  • "Zero-two" law
  • Dominant contraction
  • Positive operator

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

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