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

Title & Authors
ON A MULTI-PARAMETRIC GENERALIZATION OF THE UNIFORM ZERO-TWO LAW IN L1-SPACES
MUKHAMEDOV, FARRUKH;

Abstract
Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform "zero-two" law: let T : $\small{L^1}$(X, $\small{\mathcal{F}}$, $\small{{\mu}}$) $\small{{\rightarrow}}$ $\small{L^1}$(X, $\small{\mathcal{F}}$, $\small{{\mu}}$) be a positive contraction. If for some $\small{m{\in}{\mathbb{N}}{\cup}\{0\}}$ one has $\small{{\parallel}T^{m+1}-T^m{\parallel}}$ < 2, then $\small{\lim_{n{\rightarrow}{\infty}}{\parallel}T^{m+1}-T^m{\parallel}=0}$. 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 $\small{L^1}$-contractions.
Keywords
multi parametric;positive contraction;"zero-two" law;
Language
English
Cited by
1.
On a genaralized uniform zero-two law for positive contractions of non-commutativeL1-spaces, Journal of Physics: Conference Series, 2016, 697, 012003
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