On power bounded operators
type: Item
instance of: scholarly article
title: On power bounded operators
zbMATH Open document ID: 0611.47005
DOI: 10.1016/0022-1236(86)90101-1
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: The main result asserts that, for any contraction T on an arbitrary Banach space X, \(\| T^ n-T^{n+1}\| \to \infty\), if and only if the spectrum of T has no points on the unit circle except perhaps \(z=1\). This theorem is extended for \(\phi (T)T^ n\), where \(\phi\) is a function of spectral synthesis on the unit circle. As an application, we generalize the so-called ''zero-two'' law of Ornstein and Sucheston and Zaharopol to positive contraction on a very large class of Banach lattices.
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 3988025
zbMATH Keywords: zero-two law of Ornstein and Sucheston and Zaharopol
zbMATH Keywords: contraction
zbMATH Keywords: spectrum
zbMATH Keywords: function of spectral synthesis on the unit circle
zbMATH Keywords: Banach lattices
author: Yitzhak Katznelson
author: L. A. Tsafriri
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90101-1
OpenAlex ID: W1965156119
cites work: Support preserving measure algebras and spectral synthesis
cites work: More on the "Zero-Two" Law
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cites work: The modulus of a regular linear operator and the ''zero-two'' law in \(L^ p\)-spaces \((1<p<+\infty,p\neq 2)\)
description: scientific article; zbMATH DE number 3988025