Translator Disclaimer
July 2018 On a generalized uniform zero-two law for positive contractions of noncommutative L1-spaces and its vector-valued extension
Inomjon Ganiev, Farrukh Mukhamedov, Dilmurod Bekbaev
Banach J. Math. Anal. 12(3): 600-616 (July 2018). DOI: 10.1215/17358787-2017-0054

Abstract

Ornstein and Sucheston first proved that for a given positive contraction T:L1L1 there exists mN such that if Tm+1Tm<2, then lim nTn+1Tn=0. This result was referred to as the zero-two law. In the present article, we prove a generalized uniform zero-two law for the multiparametric family of positive contractions of noncommutative L1-spaces. Moreover, we also establish a vector-valued analogue of the uniform zero-two law for positive contractions of L1(M,Φ)—the noncommutative L1-spaces associated with center-valued traces.

Citation

Download Citation

Inomjon Ganiev. Farrukh Mukhamedov. Dilmurod Bekbaev. "On a generalized uniform zero-two law for positive contractions of noncommutative L1-spaces and its vector-valued extension." Banach J. Math. Anal. 12 (3) 600 - 616, July 2018. https://doi.org/10.1215/17358787-2017-0054

Information

Received: 2 April 2017; Accepted: 21 August 2017; Published: July 2018
First available in Project Euclid: 9 May 2018

zbMATH: 06946072
MathSciNet: MR3824742
Digital Object Identifier: 10.1215/17358787-2017-0054

Subjects:
Primary: 47A35
Secondary: 28D05, 46L52, 46L70

Rights: Copyright © 2018 Tusi Mathematical Research Group

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 3 • July 2018
Back to Top