Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\)
type: Item
instance of: scholarly article
title: Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\)
zbMATH Open document ID: 0783.47021
DOI: 10.1016/0024-3795(92)90323-3
author: Edward Bach
author: Takayuki Furuta
published in: Linear Algebra and its Applications
publication date: 1993-05-16T00:00:00Z
review text: The authors consider the equation \(T(H^{1/n} T)^ n=K\) with some natural number \(n\) and \(H\), \(K\) being positive operators on a Hilbert space (\(H\) is nonsingular). The purpose of the paper is to show that the existence of the solution \(T\) to this equation for some number \(m>0\) need not provide the solvability of the equation for any natural \(n<m\). The results continue previous investigations of the authors.
reviewed by: T. F. Filippova
Mathematics Subject Classification ID: 47A62
zbMATH DE Number: 166222
zbMATH Keywords: operator equation
zbMATH Keywords: positive operators on a Hilbert space
MaRDI profile type: Publication
full work available at URL: 0024-3795(92)90323-3
OpenAlex ID: W1989515977
Wikidata QID: Q125054855
cites work: $A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$
cites work: The operator equation \(T(H^{1/n}T)^ n=K\)
cites work: Shorter Notes: The Operator Equation THT = K
description: scientific article; zbMATH DE number 166222