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ON A MULTI-PARAMETRIC GENERALIZATION OF THE UNIFORM ZERO-TWO LAW IN L1-SPACES

Farrukh Mukhamedov
대한수학회 (The Korean Mathematical Society)|2015.11|대한수학회보 (Bulletin of the KMS)|제52권 제6호|pp. 1819-1826

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참고문헌

키워드

multi parametricpositive contraction“zero-two” law
주제분류수학

초록

Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform “zero-two” law: let T : L1(X,F,μ) → L1(X,F,μ) be a positive contraction. If for some m ∈ N∪{0} one has ∥Tm+1−Tm∥ < 2, then lim n→∞ ∥Tn+1 − Tn∥ = 0. There are many papers devoted to generalizations of this law. In the present paper we provide a multi-parametric generalization of the uniform zero-two law for L1-contractions.

Abstract

Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform “zero-two” law: let T : L1(X,F,μ) → L1(X,F,μ) be a positive contraction. If for some m ∈ N∪{0} one has ∥Tm+1−Tm∥ < 2, then lim n→∞ ∥Tn+1 − Tn∥ = 0. There are many papers devoted to generalizations of this law. In the present paper we provide a multi-parametric generalization of the uniform zero-two law for L1-contractions.

참고문헌 (21)

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