On a multi-parametric generalization of the uniform zero-two law in $L^1$-spaces
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1819-1826
https://doi.org/10.4134/BKMS.2015.52.6.1819
Published online November 30, 2015
Farrukh Mukhamedov
P.O. Box, 141, 25710, Kuantan
Abstract : Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform ``zero-two" law: let $T:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m)$ be a positive contraction. If for some $m\in\bn\cup\{0\}$ one has $\|T^{m+1}-T^m\|<2$, then $$ \lim\limits_{n\to\infty}\|T^{n+1}-T^n\|=0. $$ 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 $L^1$-contractions.
Keywords : multi parametric, positive contraction, ``zero-two" law
MSC numbers : 47A35, 17C65, 46L70, 46L52, 28D05
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd