The operator equation \(T(H^{1/n}T)^ n=K\)
type: Item
instance of: scholarly article
title: The operator equation \(T(H^{1/n}T)^ n=K\)
zbMATH Open document ID: 0664.47011
DOI: 10.1016/0024-3795(88)90205-4
author: Takayuki Furuta
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The author's summary: Let H and K be bounded positive operators on a Hilbert space, and assume that H is nonsingular. This paper shows that if there exists a positive operator T such that \(T(H^{1/n}T)^ n=K\) for some natural number n, then, for any natural number m such that \(m\leq n\) there exists a positive operator \(T_ 1\) such that \(T_ 1(H^{1/m}T_ 1)^ m=K\). In each case, there is at most one positive solution T and \(T_ 1\) respectively.
Mathematics Subject Classification ID: 47A62
zbMATH DE Number: 4086362
zbMATH Keywords: bounded positive operators on a Hilbert space
zbMATH Keywords: nonsingular
zbMATH Keywords: positive solution
reviewed by: J. Kolomý
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90205-4
OpenAlex ID: W2075380177
cites work: On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
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: Q4057176
cites work: Shorter Notes: The Operator Equation THT = K
description: scientific article; zbMATH DE number 4086362