On mixing and completely mixing properties of positive <IMG BORDER="0" SRC="/proc/2006-134-03/S0002-9939-05-08072-X/gif-title0/img1.gif" >-contractions of finite von Neumann algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On mixing and completely mixing properties of positive -contractions of finite von Neumann algebras

Authors:	Farruh Mukhamedov Seyit Temir Hasan Akin

Institution:	Department of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, 700095, Tashkent, Uzbekistan ; Department of Mathematics, Arts and Science Faculty, Harran University, 63200, Sanliurfa, Turkey ; Department of Mathematics, Arts and Science Faculty, Harran University, 63200, Sanliurfa, Turkey

Abstract:	Akcoglu and Suchaston proved the following result: Let $T: L^1(X,{\mathcal F},\mu)\to L^1(X,{\mathcal F},\mu)$ be a positive contraction. Assume that for $z\in L^1(X,{\mathcal F},\mu)$ the sequence converges weakly in $L^1(X,{\mathcal F},\mu)$ . Then either $\lim\limits_{n\to\infty}\Vert T^nz\Vert=0$ or there exists a positive function $h\in L^1(X,{\mathcal F},\mu)$ , $h\neq 0$ such that . In the paper we prove an extension of this result in a finite von Neumann algebra setting, and as a consequence we obtain that if a positive contraction of a noncommutative -space has no nonzero positive invariant element, then its mixing property implies the completely mixing property.

Keywords:	Positive contraction mixing completely mixing von Neumann algebra

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