Uniform monotonicity of norms and the strong ``zero-two'' law
type: Item
instance of: scholarly article
title: Uniform monotonicity of norms and the strong ``zero-two'' law
zbMATH Open document ID: 0688.47014
DOI: 10.1016/0022-247X(89)90240-0
author: R. Zaharopol
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Extending previous results of Ornstein-Sucheston, Katznelson-Tzafriri and Wittmann the author proves the following theorem. Let E be a Banach lattice having uniformly monotone norm and let T be a positive contraction on E. If \(\| | T^{k+1}-T^ k| \| <0\) for some \(k\in {\mathbb{N}}\), then \(\lim_{n\to \infty}\| | T^{n+1}-T^ n| \| =0.\)
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 4127929
zbMATH Keywords: Banach lattice
zbMATH Keywords: uniformly monotone norm
zbMATH Keywords: positive contraction
MaRDI profile type: Publication
cites work: Q3029575
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description: scientific article; zbMATH DE number 4127929