Hyponormal and quasinormal weighted composition operators on \(\ell ^ 2\)
type: Item
instance of: scholarly article
title: Hyponormal and quasinormal weighted composition operators on \(\ell ^ 2\)
zbMATH Open document ID: 0732.47032
author: James W. Carlson
published in: Rocky Mountain Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: For a Hilbert space H of complex-valued functions defined on a set X, a weighted composition operator T on H is usually defined by \(Tf=u(f\circ g)\) for all f in H, where u: \(X\to {\mathbb{C}}\) is a weighted function, and g: \(X\to X\) is a composition function. The author confined himself to the Hilbert space \(\ell^ 2\) of complex-valued functions defined on the integers. For a subset Y of integers, g is defined to be a composition function of Y to the integers, and u is a weighted function of integers to non-zero complex numbers, thus generalizing the usual definition of a weighted composition function. The author has characterized the normality, hyponormality and quasinormality for T and \(T^*\) with given u and g.
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 4210886
zbMATH Keywords: weighted composition operator
zbMATH Keywords: weighted function
zbMATH Keywords: composition function
zbMATH Keywords: normality
zbMATH Keywords: hyponormality
zbMATH Keywords: quasinormality
reviewed by: Shao-Chien Chang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181073115
OpenAlex ID: W1982775593
cites work: Q3317616
cites work: Hyponormal Composition Operators
DOI: 10.1216/RMJM/1181073115
description: scientific article; zbMATH DE number 4210886