Unbounded weighted shifts and subnormality
type: Item
instance of: scholarly article
title: Unbounded weighted shifts and subnormality
zbMATH Open document ID: 0675.47011
DOI: 10.1007/BF01199763
author: Jan Stochel
author: Franciszek Hugon Szafraniec
published in: Integral Equations and Operator Theory
publication date: 1989-01-01T00:00:00Z
review text: The operator \(S=(1/\sqrt{2})(x-d/dx)\) defined on the linear span of the Hermite functions is an example of an unbounded subnormal weighted shift [cf. the authors, J. Oper. Theory 14, 31--55 (1985; Zbl 0613.47022)]. It is shown that certain products of unbounded subnormal weighted shifts are again subnormal, for example the products \(R^{*pt}S^{pt}T\), \(TR^{pt}S^{*pt}\), \(TR^{*pt}S^{pt}\), \(R^{pt}S^{*pt}T\) for integers \(p\geq 0\), \(t\geq 1\) if \(R,S\) are usual weighted shifts and \(T\) is a weighted \(t\)-shift (i.e. it shifts \(t\)-times)
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 4105647
zbMATH Keywords: products of unbounded subnormal weighted shifts
zbMATH Keywords: weighted t-shift
reviewed by: Gerhard Garske
MaRDI profile type: Publication
cites work: Q4059478
cites work: Q3333590
cites work: Q4720264
cites work: Q3986910
cites work: Subnormal roots of subnormal operators
description: scientific article; zbMATH DE number 4105647