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

Farrukh Mukhamedov

doi:10.1007/s11117-010-0102-8

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

Farrukh Mukhamedov

Research output: Contribution to journal › Article › peer-review

8 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 language	English
Pages (from-to)	497-508
Number of pages	12
Journal	Positivity
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s11117-010-0102-8
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

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10.1007/s11117-010-0102-8

Cite this

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AB - 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.

KW - "Zero-two" law

KW - Dominant contraction

KW - Positive operator

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JO - Positivity

JF - Positivity

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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