Transformations having homogeneous spectra
type: Item
instance of: scholarly article
title: Transformations having homogeneous spectra
zbMATH Open document ID: 0954.37007
DOI: 10.1023/A:1021748902318
author: Valery Ryzhikov
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: Let \(T\) be an automorphism of a Lebesgue space \((X,\mu)\) and let the operator \(\widehat Tf(x):=f(Tx)\) be the operator induced by this automorphism. The main result of the paper is the statement that the map \(R:X\times X \to X\times X\) defined by the relation \(R(x,y):=(y,Tx)\) has a simple spectrum for a generic automorphism \(T\). Since the essential range of the multiplicity function of the Cartesian product \(T\times T\) is always even, the operator \(\widehat T\times\widehat T\) has a homogeneous spectrum of multiplicity two.
reviewed by: Michael L. Blank
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 1431876
zbMATH Keywords: automorphism
zbMATH Keywords: Cartesian product
zbMATH Keywords: homogeneous spectrum
MaRDI profile type: Publication
full work available at URL: a:1021748902318
OpenAlex ID: W2093443800
description: scientific article; zbMATH DE number 1431876